Annales Henri Poincaré, ISSN 1424-0637, 11/2015, Volume 16, Issue 11, pp. 2465 - 2497

The aim of this paper is twofold. First, we study eigenvalues and eigenvectors of the adjacency matrix of a bond percolation graph when the base graph is...

Continuous Spectrum | Mathematical Methods in Physics | Theoretical, Mathematical and Computational Physics | Regular Graph | Quantum Physics | Random Graph | Dynamical Systems and Ergodic Theory | Classical and Quantum Gravitation, Relativity Theory | Adjacency Matrix | Physics | Elementary Particles, Quantum Field Theory | Cayley Graph | TREE GRAPHS | STATES | PHYSICS, MULTIDISCIPLINARY | DELOCALIZATION | BETHE STRIP | PHYSICS, MATHEMATICAL | TAILED RANDOM MATRICES | ANDERSON MODEL | RANDOM SCHRODINGER-OPERATORS | EIGENVECTORS | HAMILTONIANS | ABSOLUTELY CONTINUOUS-SPECTRUM | PHYSICS, PARTICLES & FIELDS | Mathematics

Continuous Spectrum | Mathematical Methods in Physics | Theoretical, Mathematical and Computational Physics | Regular Graph | Quantum Physics | Random Graph | Dynamical Systems and Ergodic Theory | Classical and Quantum Gravitation, Relativity Theory | Adjacency Matrix | Physics | Elementary Particles, Quantum Field Theory | Cayley Graph | TREE GRAPHS | STATES | PHYSICS, MULTIDISCIPLINARY | DELOCALIZATION | BETHE STRIP | PHYSICS, MATHEMATICAL | TAILED RANDOM MATRICES | ANDERSON MODEL | RANDOM SCHRODINGER-OPERATORS | EIGENVECTORS | HAMILTONIANS | ABSOLUTELY CONTINUOUS-SPECTRUM | PHYSICS, PARTICLES & FIELDS | Mathematics

Journal Article

Communications in Mathematical Physics, ISSN 0010-3616, 08/2017, Volume 354, Issue 1, pp. 115 - 159

We prove that the eigenvectors associated to small enough eigenvalues of a heavy-tailed symmetric random matrix are delocalized with probability tending to one...

LOCALIZATION | RANDOM SCHRODINGER-OPERATORS | EIGENVECTORS | DISORDER | SEMICIRCLE LAW | SPECTRUM | BAND | PHYSICS, MATHEMATICAL | Probability | Mathematics

LOCALIZATION | RANDOM SCHRODINGER-OPERATORS | EIGENVECTORS | DISORDER | SEMICIRCLE LAW | SPECTRUM | BAND | PHYSICS, MATHEMATICAL | Probability | Mathematics

Journal Article

Probability Theory and Related Fields, ISSN 0178-8051, 12/2013, Volume 157, Issue 3, pp. 885 - 953

Consider an $$n \times n$$ Hermitian random matrix with, above the diagonal, independent entries with $$\alpha $$ -stable symmetric distribution and $$0 <...

Eigenvector delocalization | Random matrices | Mathematical and Computational Biology | Statistics for Business/Economics/Mathematical Finance/Insurance | Theoretical, Mathematical and Computational Physics | Operations Research/Decision Theory | Probability Theory and Stochastic Processes | Mathematics | 15B52 (60B20, 60F15, 60E07) | Quantitative Finance | Wegner estimate | Stable distribution | UNIVERSALITY | STATISTICS | SEMICIRCLE LAW | STATISTICS & PROBABILITY | SPECTRUM | Studies | Probability | Mathematical models | Convergence

Eigenvector delocalization | Random matrices | Mathematical and Computational Biology | Statistics for Business/Economics/Mathematical Finance/Insurance | Theoretical, Mathematical and Computational Physics | Operations Research/Decision Theory | Probability Theory and Stochastic Processes | Mathematics | 15B52 (60B20, 60F15, 60E07) | Quantitative Finance | Wegner estimate | Stable distribution | UNIVERSALITY | STATISTICS | SEMICIRCLE LAW | STATISTICS & PROBABILITY | SPECTRUM | Studies | Probability | Mathematical models | Convergence

Journal Article

Probability Theory and Related Fields, ISSN 0178-8051, 02/2019, Volume 173, Issue 1-2, pp. 261 - 292

We study convergence to equilibrium for a class of Markov chains in random environment. The chains are sparse in the sense that in every row of the transition...

STATISTICS & PROBABILITY | RANDOM RANDOM-WALKS | BIRTH | Markov processes | Analysis | Cut-off | Random walk | Markov chains | Dirichlet problem | Graph theory | Markov analysis | Trajectory analysis | Equilibrium | Mathematics

STATISTICS & PROBABILITY | RANDOM RANDOM-WALKS | BIRTH | Markov processes | Analysis | Cut-off | Random walk | Markov chains | Dirichlet problem | Graph theory | Markov analysis | Trajectory analysis | Equilibrium | Mathematics

Journal Article

Electronic Journal of Probability, ISSN 1083-6489, 02/2014, Volume 19, pp. 1 - 33

We consider the spreading dynamics of two nested invasion clusters on an infinite tree. This model was defined as the chase-escape model by Kordzakhia and it...

SIR models | Branching processes | Predator-prey dynamics | predator-prey dynamics | SURVIVAL PROBABILITY | STATISTICS & PROBABILITY | ASYMPTOTICS | MODEL | branching processes | Mathematics - Probability | Probability | Mathematics

SIR models | Branching processes | Predator-prey dynamics | predator-prey dynamics | SURVIVAL PROBABILITY | STATISTICS & PROBABILITY | ASYMPTOTICS | MODEL | branching processes | Mathematics - Probability | Probability | Mathematics

Journal Article

Probability Theory and Related Fields, ISSN 0178-8051, 4/2018, Volume 170, Issue 3, pp. 933 - 960

A finite ergodic Markov chain exhibits cutoff if its distance to equilibrium remains close to its initial value over a certain number of iterations and then...

Mathematical and Computational Biology | Statistics for Business/Economics/Mathematical Finance/Insurance | Theoretical, Mathematical and Computational Physics | Operations Research/Decision Theory | Primary 05C80 | Probability Theory and Stochastic Processes | Mathematics | 05C81 | Quantitative Finance | MARTINGALES | RANDOM REGULAR GRAPHS | CONTINUITY | TAIL PROBABILITIES | MARKOV-CHAINS | THEOREM | COVER TIME | MIXING TIME | STATISTICS & PROBABILITY | CRITICAL RANDOM GRAPHS | GIANT COMPONENT | Markov processes | Analysis | Markov chains | Random walk theory | Graph theory | Equilibrium | Random walk

Mathematical and Computational Biology | Statistics for Business/Economics/Mathematical Finance/Insurance | Theoretical, Mathematical and Computational Physics | Operations Research/Decision Theory | Primary 05C80 | Probability Theory and Stochastic Processes | Mathematics | 05C81 | Quantitative Finance | MARTINGALES | RANDOM REGULAR GRAPHS | CONTINUITY | TAIL PROBABILITIES | MARKOV-CHAINS | THEOREM | COVER TIME | MIXING TIME | STATISTICS & PROBABILITY | CRITICAL RANDOM GRAPHS | GIANT COMPONENT | Markov processes | Analysis | Markov chains | Random walk theory | Graph theory | Equilibrium | Random walk

Journal Article

Electronic Communications in Probability, ISSN 1083-589X, 2011, Volume 16, pp. 104 - 113

In this note, we revisit the work of T. Tao and V. Vu on large non-hermitian random matrices with independent and identically distributed (i.i.d.) entries with...

Spherical law | Generalized eigenvalues | Non-hermitian random matrices | generalized eigenvalues | CIRCULAR LAW | STATISTICS & PROBABILITY | non-hermitian random matrices | spherical law

Spherical law | Generalized eigenvalues | Non-hermitian random matrices | generalized eigenvalues | CIRCULAR LAW | STATISTICS & PROBABILITY | non-hermitian random matrices | spherical law

Journal Article

Journal of Combinatorial Theory, Series B, ISSN 0095-8956, 09/2019, Volume 138, pp. 196 - 205

Given a collection of n rooted trees with depth h, we give a necessary and sufficient condition for this collection to be the collection of h-depth universal...

Erdös–Gallai theorem | Universal covering | Degree sequence | MATHEMATICS | Erdos-Gallai theorem | Combinatorics | Mathematics

Erdös–Gallai theorem | Universal covering | Degree sequence | MATHEMATICS | Erdos-Gallai theorem | Combinatorics | Mathematics

Journal Article

Communications on Pure and Applied Mathematics, ISSN 0010-3640, 11/2016, Volume 69, Issue 11, pp. 2131 - 2194

We consider a square random matrix of size N of the form A + Y where A is deterministic and Y has i.i.d. entries with variance 1/N. Under mild assumptions, as...

SPECTRAL DISTRIBUTION | MATHEMATICS | UNIVERSALITY | MATHEMATICS, APPLIED | PERTURBATIONS | NORM | LIMIT | VALUES | FINITE RANK DEFORMATIONS | ZEROS | Probability | Mathematics

SPECTRAL DISTRIBUTION | MATHEMATICS | UNIVERSALITY | MATHEMATICS, APPLIED | PERTURBATIONS | NORM | LIMIT | VALUES | FINITE RANK DEFORMATIONS | ZEROS | Probability | Mathematics

Journal Article

Probability Theory and Related Fields, ISSN 0178-8051, 10/2015, Volume 163, Issue 1-2, pp. 149 - 222

Consider the ErdAs-Renyi random graph on vertices where each edge is present independently with probability , with fixed. For large , a typical random graph...

Configuration model | Random graphs | Entropy | Large deviations | Unimodular measure | Local convergence | Random trees | CONVERGENT SEQUENCES | STATISTICS & PROBABILITY | PRINCIPLE | Studies | Graph theory | Probability distribution | Mathematical models | Decision trees | Trees | Mathematical analysis | Texts | Graphs | Deviation | Convergence | Mathematics

Configuration model | Random graphs | Entropy | Large deviations | Unimodular measure | Local convergence | Random trees | CONVERGENT SEQUENCES | STATISTICS & PROBABILITY | PRINCIPLE | Studies | Graph theory | Probability distribution | Mathematical models | Decision trees | Trees | Mathematical analysis | Texts | Graphs | Deviation | Convergence | Mathematics

Journal Article

Electronic Communications in Probability, ISSN 1083-589X, 04/2013, Volume 18, pp. 1 - 8

In this note, we study the n x n random Euclidean matrix whose entry (i, j) is equal to f (parallel to X-i - X-j parallel to) for some function f and the X-i's...

Marcenko-Pastur distribution | Euclidean random matrices | Log-concave distribution | EIGENVALUES | STATISTICS & PROBABILITY | SPECTRUM | Probability | Mathematics

Marcenko-Pastur distribution | Euclidean random matrices | Log-concave distribution | EIGENVALUES | STATISTICS & PROBABILITY | SPECTRUM | Probability | Mathematics

Journal Article

The Annals of Probability, ISSN 0091-1798, 11/2014, Volume 42, Issue 6, pp. 2454 - 2496

We consider n × n Hermitian matrices with i.i.d. entries Xij whose tail probabilities ℙ(|Xij| ≥ t) behave like e−atα for some a > 0 and α ∈ (0, 2). We...

Topological compactness | Integers | Equivalence relation | Eigenvalues | Matrices | Topology | Random variables | Spectral graph theory | Vertices | Topological spaces | Local weak convergence | Random matrices | Spectral measure | Large deviations | Random networks | Free convolution | large deviations | local weak convergence | random networks | free convolution | SEMICIRCULAR DISTRIBUTION | STATISTICS & PROBABILITY | RANDOM GRAPHS | spectral measure | Mathematics - Probability | Mathematics | 60B20 | 47A10 | 15A18

Topological compactness | Integers | Equivalence relation | Eigenvalues | Matrices | Topology | Random variables | Spectral graph theory | Vertices | Topological spaces | Local weak convergence | Random matrices | Spectral measure | Large deviations | Random networks | Free convolution | large deviations | local weak convergence | random networks | free convolution | SEMICIRCULAR DISTRIBUTION | STATISTICS & PROBABILITY | RANDOM GRAPHS | spectral measure | Mathematics - Probability | Mathematics | 60B20 | 47A10 | 15A18

Journal Article

British Journal of Haematology, ISSN 0007-1048, 01/2020, Volume 188, Issue 2, pp. 268 - 271

Summary We analysed the outcomes of 62 patients with refractory/relapsed diffuse large B‐cell lymphoma (rrDLBCL) who had pre‐transplantation fluorodeoxyglucose...

transplant | positron emission tomography/computed tomography | diffuse large B‐cell lymphoma | 18‐ fluorodeoxyglucose | autologous stem cell transplantation | computed tomography | 18-fluorodeoxyglucose | RESPONSE ASSESSMENT | diffuse large B-cell lymphoma | HODGKINS | SCAN | positron emission tomography | HEMATOLOGY | PET | Dexamethasone | Transplants & implants | Positron emission | Rituximab | Transplantation | Survival | Lymphoma | Emissions | Chemotherapy | Cytarabine | Computed tomography | Tomography | Glycolysis | Carboplatin | Lymphomas | Positron emission tomography

transplant | positron emission tomography/computed tomography | diffuse large B‐cell lymphoma | 18‐ fluorodeoxyglucose | autologous stem cell transplantation | computed tomography | 18-fluorodeoxyglucose | RESPONSE ASSESSMENT | diffuse large B-cell lymphoma | HODGKINS | SCAN | positron emission tomography | HEMATOLOGY | PET | Dexamethasone | Transplants & implants | Positron emission | Rituximab | Transplantation | Survival | Lymphoma | Emissions | Chemotherapy | Cytarabine | Computed tomography | Tomography | Glycolysis | Carboplatin | Lymphomas | Positron emission tomography

Journal Article

Clinical Endocrinology, ISSN 0300-0664, 08/2018, Volume 89, Issue 2, pp. 148 - 154

Summary Objective Osteoporotic fractures associated with Cushing's syndrome (CS) may occur despite normal bone mineral density (BMD). Few studies have...

bone mineral density | trabecular bone score | Cushing's syndrome | adrenal incidentaloma | osteoporosis | subclinical hypercortisolism | bone microarchitecture | GLUCOCORTICOID-INDUCED OSTEOPOROSIS | ADRENAL INCIDENTALOMAS | MINERAL DENSITY | THERAPY | LUMBAR SPINE | DISEASE | ENDOCRINOLOGY & METABOLISM | WHITE WOMEN | FRACTURES | CLINICAL-PRACTICE | Vertebrae | Nervous system diseases | Glucocorticoids | Secretion | Hyperplasia | Hydrocortisone | Bone (trabecular) | Osteoporosis | Adrenocorticotropic hormone | Fractures | Pituitary | Conditioned stimulus | Remission | Bone mineral density

bone mineral density | trabecular bone score | Cushing's syndrome | adrenal incidentaloma | osteoporosis | subclinical hypercortisolism | bone microarchitecture | GLUCOCORTICOID-INDUCED OSTEOPOROSIS | ADRENAL INCIDENTALOMAS | MINERAL DENSITY | THERAPY | LUMBAR SPINE | DISEASE | ENDOCRINOLOGY & METABOLISM | WHITE WOMEN | FRACTURES | CLINICAL-PRACTICE | Vertebrae | Nervous system diseases | Glucocorticoids | Secretion | Hyperplasia | Hydrocortisone | Bone (trabecular) | Osteoporosis | Adrenocorticotropic hormone | Fractures | Pituitary | Conditioned stimulus | Remission | Bone mineral density

Journal Article

ANNALS OF PROBABILITY, ISSN 0091-1798, 05/2019, Volume 47, Issue 3, pp. 1653 - 1676

We consider inhomogeneous Erdos-Renyi graphs. We suppose that the maximal mean degree d satisfies d << log n. We characterise the asymptotic behaviour of the...

extreme eigenvalues | Erdos-Renyi graph | STATISTICS & PROBABILITY | random matrices | Probability | Mathematics

extreme eigenvalues | Erdos-Renyi graph | STATISTICS & PROBABILITY | random matrices | Probability | Mathematics

Journal Article

Random Structures & Algorithms, ISSN 1042-9832, 12/2008, Volume 33, Issue 4, pp. 515 - 532

We study the spectral measure of large Euclidean random matrices. The entries of these matrices are determined by the relative position of n random points in a...

random matrix | spatial point process | random geometric graphs | Euclidean distance matrix | spectral measure | Random matrix | Spectral measure | Random geometric graphs | Spatial point process | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS | MATHEMATICS, APPLIED | SPECTRA

random matrix | spatial point process | random geometric graphs | Euclidean distance matrix | spectral measure | Random matrix | Spectral measure | Random geometric graphs | Spatial point process | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS | MATHEMATICS, APPLIED | SPECTRA

Journal Article

Probability Theory and Related Fields, ISSN 0178-8051, 10/2013, Volume 157, Issue 1, pp. 183 - 208

Elek and Lippner (Proc. Am. Math. Soc. 138(8), 2939–2947, 2010) showed that the convergence of a sequence of bounded-degree graphs implies the existence of a...

Primary 60C05 | Secondary 82B20 | Mathematical and Computational Biology | Theoretical, Mathematical and Computational Physics | Probability Theory and Stochastic Processes | Mathematics | Heilmann-Lieb Theorem | 05C80 | Quantitative Finance | Matching | Statistics for Business/Economics/Mathematical Finance/Insurance | Operations Research/Decision Theory | Local weak convergence | Random sparse graphs | LIMITS | MAXIMUM MATCHINGS | STATISTICS & PROBABILITY | KARP-SIPSER | Graphs | Probability distribution | Theory | Asymptotic properties | Mathematical analysis | Covering | Recursion | Constraining | Convergence | Probability

Primary 60C05 | Secondary 82B20 | Mathematical and Computational Biology | Theoretical, Mathematical and Computational Physics | Probability Theory and Stochastic Processes | Mathematics | Heilmann-Lieb Theorem | 05C80 | Quantitative Finance | Matching | Statistics for Business/Economics/Mathematical Finance/Insurance | Operations Research/Decision Theory | Local weak convergence | Random sparse graphs | LIMITS | MAXIMUM MATCHINGS | STATISTICS & PROBABILITY | KARP-SIPSER | Graphs | Probability distribution | Theory | Asymptotic properties | Mathematical analysis | Covering | Recursion | Constraining | Convergence | Probability

Journal Article

IEEE Transactions on Information Theory, ISSN 0018-9448, 09/2012, Volume 58, Issue 9, pp. 5841 - 5855

We analyze the stability of standard, buffered, slotted-Aloha systems. Specifically, we consider a set of N users, each equipped with an infinite buffer....

Asymptotic stability | Atmospheric measurements | Stability criteria | mean-field asymptotics | Markov processes | random multiple access | Aloha | Approximation methods | Numerical stability | stability | MULTIPLE-ACCESS | INTERACTING QUEUES | COMPUTER SCIENCE, INFORMATION SYSTEMS | RANDOM-ACCESS SYSTEMS | ENGINEERING, ELECTRICAL & ELECTRONIC | Stability | Approximation | Asymptotic properties | Packet transmission | Buffers | Channels | Standards | Extreme values | Engineering and Technology | Elektroteknik och elektronik | Electrical Engineering, Electronic Engineering, Information Engineering | Teknik och teknologier

Asymptotic stability | Atmospheric measurements | Stability criteria | mean-field asymptotics | Markov processes | random multiple access | Aloha | Approximation methods | Numerical stability | stability | MULTIPLE-ACCESS | INTERACTING QUEUES | COMPUTER SCIENCE, INFORMATION SYSTEMS | RANDOM-ACCESS SYSTEMS | ENGINEERING, ELECTRICAL & ELECTRONIC | Stability | Approximation | Asymptotic properties | Packet transmission | Buffers | Channels | Standards | Extreme values | Engineering and Technology | Elektroteknik och elektronik | Electrical Engineering, Electronic Engineering, Information Engineering | Teknik och teknologier

Journal Article

Probability Theory and Related Fields, ISSN 0178-8051, 4/2012, Volume 152, Issue 3, pp. 751 - 779

Let (X jk ) jk≥1 be i.i.d. nonnegative random variables with bounded density, mean m, and finite positive variance σ 2. Let M be the n × n random Markov matrix...

Mathematical and Computational Biology | Theoretical, Mathematical and Computational Physics | Stochastic matrices | Probability Theory and Stochastic Processes | Markov chains | Mathematics | Quantitative Finance | Spectrum | 15A52 | Random matrices | Statistics for Business/Economics/Mathematical Finance/Insurance | Operations Research/Decision Theory | Eigenvalues | BEHAVIOR | SINGULAR-VALUES | STATISTICS & PROBABILITY | Markov processes | Laws, regulations and rules | Studies | Stochastic models | Mathematical analysis | Eigen values | Law | Dirichlet problem | Matrices | Matrix methods | Density | Probability | Spectral Theory

Mathematical and Computational Biology | Theoretical, Mathematical and Computational Physics | Stochastic matrices | Probability Theory and Stochastic Processes | Markov chains | Mathematics | Quantitative Finance | Spectrum | 15A52 | Random matrices | Statistics for Business/Economics/Mathematical Finance/Insurance | Operations Research/Decision Theory | Eigenvalues | BEHAVIOR | SINGULAR-VALUES | STATISTICS & PROBABILITY | Markov processes | Laws, regulations and rules | Studies | Stochastic models | Mathematical analysis | Eigen values | Law | Dirichlet problem | Matrices | Matrix methods | Density | Probability | Spectral Theory

Journal Article