Journal of Statistical Physics, ISSN 0022-4715, 11/2015, Volume 161, Issue 3, pp. 577 - 597

We study asymptotics of the free energy for the directed polymer in random environment. The polymer is allowed to make unbounded jumps and the environment is...

Ground states | Theoretical, Mathematical and Computational Physics | Quantum Physics | First passage percolation | 82D30 | Statistical Physics, Dynamical Systems and Complexity | Physics | 82A51 | Zero temperature | Random environment | Secondary: 60K35 | Physical Chemistry | Directed polymer | Primary: 60K37 | FIRST-PASSAGE PERCOLATION | TIME CONSTANT | LOCALIZATION | PHYSICS, MATHEMATICAL | PARABOLIC ANDERSON MODEL | 1ST-PASSAGE PERCOLATION | PROBABILITY | GROWTH | DISORDER | LYAPUNOV EXPONENT | Polymers | Usage | Polymer industry | Probability | Mathematics

Ground states | Theoretical, Mathematical and Computational Physics | Quantum Physics | First passage percolation | 82D30 | Statistical Physics, Dynamical Systems and Complexity | Physics | 82A51 | Zero temperature | Random environment | Secondary: 60K35 | Physical Chemistry | Directed polymer | Primary: 60K37 | FIRST-PASSAGE PERCOLATION | TIME CONSTANT | LOCALIZATION | PHYSICS, MATHEMATICAL | PARABOLIC ANDERSON MODEL | 1ST-PASSAGE PERCOLATION | PROBABILITY | GROWTH | DISORDER | LYAPUNOV EXPONENT | Polymers | Usage | Polymer industry | Probability | Mathematics

Journal Article

Probability Theory and Related Fields, ISSN 0178-8051, 06/2016, Volume 165, Issue 1-2, pp. 401 - 445

To access, purchase, authenticate, or subscribe to the full-text of this article, please visit this link: http://dx.doi.org/10.1007/s00440-015-0634-8 The...

Primary 60K35 | Secondary 82D30 | Spin glasses | Models | Statistics | Analysis

Primary 60K35 | Secondary 82D30 | Spin glasses | Models | Statistics | Analysis

Journal Article

Communications in Mathematical Physics, ISSN 0010-3616, 10/2013, Volume 323, Issue 1, pp. 417 - 447

We study a model of directed polymers in random environment in dimension 1 + d, given by a Brownian motion in a Poissonian potential. We study the effect of...

Quantum Physics | Statistical Physics, Dynamical Systems and Complexity | Mathematical Physics | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Physics | DIRECTED POLYMERS | TIME | PHYSICS, MATHEMATICAL | PARTITION-FUNCTION | RANDOM ENVIRONMENT | Polymers | Analysis | Polymer industry | Mathematics - Probability | Probability | Mathematics

Quantum Physics | Statistical Physics, Dynamical Systems and Complexity | Mathematical Physics | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Physics | DIRECTED POLYMERS | TIME | PHYSICS, MATHEMATICAL | PARTITION-FUNCTION | RANDOM ENVIRONMENT | Polymers | Analysis | Polymer industry | Mathematics - Probability | Probability | Mathematics

Journal Article

Inventiones mathematicae, ISSN 0020-9910, 10/2017, Volume 210, Issue 1, pp. 135 - 209

We analyze the statics for pure p-spin spherical spin glass models with $$p\ge 3$$ p ≥ 3 , at low enough temperature. With $$F_{N,\beta }$$ F N , β denoting...

60G60 | Mathematics, general | Primary 60G15 | Mathematics | 82D30 | Secondary 60B20 | MATHEMATICS | CHAOS | TEMPERATURE | FLUCTUATIONS | COMPLEXITY | MODEL | FREE-ENERGY | Spin glasses | Analysis | Mathematics - Probability

60G60 | Mathematics, general | Primary 60G15 | Mathematics | 82D30 | Secondary 60B20 | MATHEMATICS | CHAOS | TEMPERATURE | FLUCTUATIONS | COMPLEXITY | MODEL | FREE-ENERGY | Spin glasses | Analysis | Mathematics - Probability

Journal Article

5.
Full Text
Stability of point defects of degree ±12 in a two-dimensional nematic liquid crystal model

Calculus of Variations and Partial Differential Equations, ISSN 0944-2669, 10/2016, Volume 55, Issue 5

Journal Article

Journal of Statistical Physics, ISSN 0022-4715, 1/2019, Volume 174, Issue 2, pp. 259 - 275

In this paper, we study some properties of optimal paths in the first passage percolation on $$\mathbb {Z}^d$$ Z d and show the following: (i) the number of...

Theoretical, Mathematical and Computational Physics | Primary 60K37 | Random geometry | Quantum Physics | First passage percolation | 82D30 | Physics | Statistical Physics and Dynamical Systems | 82A51 | Random environment | Physical Chemistry | Geodesics | Secondary 60K35 | PHYSICS, MATHEMATICAL

Theoretical, Mathematical and Computational Physics | Primary 60K37 | Random geometry | Quantum Physics | First passage percolation | 82D30 | Physics | Statistical Physics and Dynamical Systems | 82A51 | Random environment | Physical Chemistry | Geodesics | Secondary 60K35 | PHYSICS, MATHEMATICAL

Journal Article

Journal of Statistical Physics, ISSN 0022-4715, 10/2018, Volume 173, Issue 2, pp. 249 - 267

In this note we prove a correlation inequality for local variables of a Gibbs field based on the connectivity in a random cluster representation of the non...

Spin glasses | Random cluster representation | 82B44 | Theoretical, Mathematical and Computational Physics | 60G60 | Correlation inequalities | Disagreement percolation | Quantum Physics | 82D30 | Physics | Statistical Physics and Dynamical Systems | Physical Chemistry | Gibbs fields | 60J99 | PERCOLATION | PHYSICS, MATHEMATICAL | Analysis | Mathematics - Probability

Spin glasses | Random cluster representation | 82B44 | Theoretical, Mathematical and Computational Physics | 60G60 | Correlation inequalities | Disagreement percolation | Quantum Physics | 82D30 | Physics | Statistical Physics and Dynamical Systems | Physical Chemistry | Gibbs fields | 60J99 | PERCOLATION | PHYSICS, MATHEMATICAL | Analysis | Mathematics - Probability

Journal Article

Calculus of Variations and Partial Differential Equations, ISSN 0944-2669, 10/2018, Volume 57, Issue 5, pp. 1 - 19

In this paper, we investigate the structure of local minimizers for the isotropic–nematic interface based on the Landau-de Gennes energy. In the absence of the...

35J61 | Systems Theory, Control | Calculus of Variations and Optimal Control; Optimization | Analysis | Theoretical, Mathematical and Computational Physics | Mathematics | 82D30 | 35J47

35J61 | Systems Theory, Control | Calculus of Variations and Optimal Control; Optimization | Analysis | Theoretical, Mathematical and Computational Physics | Mathematics | 82D30 | 35J47

Journal Article

The Annals of Probability, ISSN 0091-1798, 11/2013, Volume 41, Issue 6, pp. 4214 - 4247

We analyze the landscape of general smooth Gaussian functions on the sphere in dimension N, when N is large. We give an explicit formula for the asymptotic...

Local minimum | Integers | Spin glasses | Infinity | Critical points | Critical values | Eigenvalues | Mathematical functions | Random variables | Random matrices | Parisi formula | Sample | STATISTICS & PROBABILITY | critical points | random matrices | spin glasses | 15A52 | 60G60 | 82D30

Local minimum | Integers | Spin glasses | Infinity | Critical points | Critical values | Eigenvalues | Mathematical functions | Random variables | Random matrices | Parisi formula | Sample | STATISTICS & PROBABILITY | critical points | random matrices | spin glasses | 15A52 | 60G60 | 82D30

Journal Article

Journal of Statistical Physics, ISSN 0022-4715, 05/2018, Volume 171, Issue 4, pp. 656 - 678

We consider a random walk in dimension in a dynamic random environment evolving as an interchange process with rate . We prove that, if we choose large enough,...

Interchange process | Limit theorems | Dynamic random environment | Random walk | Renormalisation | DYNAMIC RANDOM-ENVIRONMENTS | LARGE NUMBERS | LAW | PHYSICS, MATHEMATICAL | Mathematics - Probability | Probability | Mathematics

Interchange process | Limit theorems | Dynamic random environment | Random walk | Renormalisation | DYNAMIC RANDOM-ENVIRONMENTS | LARGE NUMBERS | LAW | PHYSICS, MATHEMATICAL | Mathematics - Probability | Probability | Mathematics

Journal Article

Proceedings of the American Mathematical Society, ISSN 0002-9939, 07/2016, Volume 144, Issue 7, pp. 3135 - 3150

G. Parisi predicted an important variational formula for the thermodynamic limit of the intensive free energy for a class of mean field spin glasses. In this...

Parisi formula | Sherrington-Kirkpatrick model | Dynamic programming | MATHEMATICS | dynamic programming | MATHEMATICS, APPLIED | FORMULA

Parisi formula | Sherrington-Kirkpatrick model | Dynamic programming | MATHEMATICS | dynamic programming | MATHEMATICS, APPLIED | FORMULA

Journal Article

Annals of Probability, ISSN 0091-1798, 03/2018, Volume 46, Issue 2, pp. 605 - 686

We consider biased random walks in positive random conductances on the d-dimensional lattice in the zero-speed regime and study their scaling limits. We obtain...

Random walks in random environments | Trap model | Zero-speed | Scaling limit | Random conductances | SPEED | DIFFUSIONS | scaling limit | PERCOLATION | DYNAMICS | CONVERGENCE | STATISTICS & PROBABILITY | random conductances | trap model | zero-speed | QUENCHED INVARIANCE-PRINCIPLES

Random walks in random environments | Trap model | Zero-speed | Scaling limit | Random conductances | SPEED | DIFFUSIONS | scaling limit | PERCOLATION | DYNAMICS | CONVERGENCE | STATISTICS & PROBABILITY | random conductances | trap model | zero-speed | QUENCHED INVARIANCE-PRINCIPLES

Journal Article

Probability Theory and Related Fields, ISSN 0178-8051, 6/2019, Volume 174, Issue 1, pp. 553 - 646

We prove that, after suitable rescaling, the simple random walk on the trace of a large critical branching random walk in $$\mathbb {Z}^d$$ Z d converges to...

Statistics for Business, Management, Economics, Finance, Insurance | Secondary 82D30 | Spatial tree | Mathematical and Computational Biology | Theoretical, Mathematical and Computational Physics | Random walk | Branching random walk | Primary 60K37 | Probability Theory and Stochastic Processes | Mathematics | Quantitative Finance | Super-process | Random environments | Operations Research/Decision Theory | STATISTICS & PROBABILITY | Random 7walk | Labyrinth | Random walk theory | Rescaling | Brownian movements

Statistics for Business, Management, Economics, Finance, Insurance | Secondary 82D30 | Spatial tree | Mathematical and Computational Biology | Theoretical, Mathematical and Computational Physics | Random walk | Branching random walk | Primary 60K37 | Probability Theory and Stochastic Processes | Mathematics | Quantitative Finance | Super-process | Random environments | Operations Research/Decision Theory | STATISTICS & PROBABILITY | Random 7walk | Labyrinth | Random walk theory | Rescaling | Brownian movements

Journal Article

Journal of Statistical Physics, ISSN 0022-4715, 6/2015, Volume 159, Issue 6, pp. 1306 - 1326

We consider the quadratic optimization problem $$\begin{aligned}F_n^{W,\mathbf{h}}:= \sup _{\mathbf{x}\in S^{n-1}} \left( \frac{1}{2} \mathbf{x}^T W...

Random matrices | 60F10 | Physical Chemistry | Theoretical, Mathematical and Computational Physics | Quantum Physics | Large deviations | 82D30 | Statistical Physics, Dynamical Systems and Complexity | Replica method | Spin glass | Physics | PHYSICS, MATHEMATICAL | Mathematics - Probability

Random matrices | 60F10 | Physical Chemistry | Theoretical, Mathematical and Computational Physics | Quantum Physics | Large deviations | 82D30 | Statistical Physics, Dynamical Systems and Complexity | Replica method | Spin glass | Physics | PHYSICS, MATHEMATICAL | Mathematics - Probability

Journal Article

Annales Henri Poincaré, ISSN 1424-0637, 8/2019, Volume 20, Issue 8, pp. 2819 - 2872

We consider the athermal quasi-static dynamics (AQS) of disordered systems driven by an external field. Our interest is in an automaton description (AQS-A)...

Mathematical Methods in Physics | Secondary 82C44 | Theoretical, Mathematical and Computational Physics | Primary 82D30 | Quantum Physics | Dynamical Systems and Ergodic Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | DENSITY | DYNAMICS | PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL | HYSTERESIS | PHYSICS, PARTICLES & FIELDS | Robots

Mathematical Methods in Physics | Secondary 82C44 | Theoretical, Mathematical and Computational Physics | Primary 82D30 | Quantum Physics | Dynamical Systems and Ergodic Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | DENSITY | DYNAMICS | PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL | HYSTERESIS | PHYSICS, PARTICLES & FIELDS | Robots

Journal Article

Annales de l'institut Henri Poincare (B) Probability and Statistics, ISSN 0246-0203, 02/2018, Volume 54, Issue 1, pp. 363 - 384

We prove a quenched central limit theorem for balanced random walks in time-dependent ergodic random environments which is not necessarily nearest-neighbor. We...

Random walk in random environment | Maximum principle | Quenched central limit theorem | PARABOLIC DIFFERENCE-OPERATORS | STOCHASTIC HOMOGENIZATION | BALLISTIC RANDOM-WALKS | EQUATIONS | STATISTICS & PROBABILITY | ZERO-RANGE PROCESS

Random walk in random environment | Maximum principle | Quenched central limit theorem | PARABOLIC DIFFERENCE-OPERATORS | STOCHASTIC HOMOGENIZATION | BALLISTIC RANDOM-WALKS | EQUATIONS | STATISTICS & PROBABILITY | ZERO-RANGE PROCESS

Journal Article

Calculus of Variations and Partial Differential Equations, ISSN 0944-2669, 4/2017, Volume 56, Issue 2, pp. 1 - 15

In this paper, we investigate the structure and stability of the isotropic-nematic interface in 1-D. In the absence of the anisotropic energy, the uniaxial...

35A15 | Systems Theory, Control | Calculus of Variations and Optimal Control; Optimization | Analysis | Theoretical, Mathematical and Computational Physics | 76A15 | Mathematics | 82D30 | 35J57 | MATHEMATICS | MATHEMATICS, APPLIED | PHASE | HARD SPHEROCYLINDERS | LIQUID-CRYSTALS | Anisotropy

35A15 | Systems Theory, Control | Calculus of Variations and Optimal Control; Optimization | Analysis | Theoretical, Mathematical and Computational Physics | 76A15 | Mathematics | 82D30 | 35J57 | MATHEMATICS | MATHEMATICS, APPLIED | PHASE | HARD SPHEROCYLINDERS | LIQUID-CRYSTALS | Anisotropy

Journal Article

The Annals of Applied Probability, ISSN 1050-5164, 8/2008, Volume 18, Issue 4, pp. 1619 - 1635

We consider branching random walks in d-dimensional integer lattice with time-space i.i.d. offspring distributions. When d ≥ 3 and the fluctuation of the...

Comets | Transition probabilities | Population growth | Central limit theorem | Random walk | Randomness | Markov chains | Polymers | Martingales | Random environment | Branching random walk | Directed polymers | Phase transition | central limit theorem | random environment | DISORDER | branching random walk | STATISTICS & PROBABILITY | DIFFUSION | phase transition | directed polymers | 60J80 | 60K37 | 82D30 | 60K35 | 60F05

Comets | Transition probabilities | Population growth | Central limit theorem | Random walk | Randomness | Markov chains | Polymers | Martingales | Random environment | Branching random walk | Directed polymers | Phase transition | central limit theorem | random environment | DISORDER | branching random walk | STATISTICS & PROBABILITY | DIFFUSION | phase transition | directed polymers | 60J80 | 60K37 | 82D30 | 60K35 | 60F05

Journal Article

The Annals of Applied Probability, ISSN 1050-5164, 2/2015, Volume 25, Issue 1, pp. 116 - 149

We study existence of random elements with partially specified distributions. The technique relies on the existence of a positive extension for linear...

Correlation measure | Contact distribution function | Random closed set | Point process | Two-point covering probability | Realisability | 2-PHASE RANDOM-MEDIA | correlation measure | SUFFICIENT CONDITIONS | random closed set | STATISTICS & PROBABILITY | two-point covering probability | contact distribution function | realisability | 60D05 | 60G55 | 47B65 | 82D30 | 46A40 | 28C05 | 74A40

Correlation measure | Contact distribution function | Random closed set | Point process | Two-point covering probability | Realisability | 2-PHASE RANDOM-MEDIA | correlation measure | SUFFICIENT CONDITIONS | random closed set | STATISTICS & PROBABILITY | two-point covering probability | contact distribution function | realisability | 60D05 | 60G55 | 47B65 | 82D30 | 46A40 | 28C05 | 74A40

Journal Article

Stochastic Processes and their Applications, ISSN 0304-4149, 2009, Volume 119, Issue 10, pp. 3101 - 3132

We first obtain exponential inequalities for martingales. Let be a sequence of martingale differences relative to a filtration and set . We prove that if for...

Supermartingales | Multiplicative cascades | Random environment | Hoeffding and Azuma’s inequality | Large deviation inequality | Martingale differences | Exponential inequality | Directed polymers | Convergence rate | Bernstein’s inequality | Concentration inequality | Free energy | Hoeffding and Azuma's inequality | Bernstein's inequality | STATISTICS & PROBABILITY | STRONG DISORDER | ITERATED RANDOM MULTIPLICATIONS | DIFFUSION | INVARIANT DISTRIBUTIONS | LARGE DEVIATIONS | Martingale differences Supermartingales Large deviation inequality Exponential inequality Bernstein's inequality Hoeffding and Azuma's inequality Directed polymers Random environment Concentration inequality Free energy Convergence rate Multiplicative cascades | Polymers | Analysis | Mathematics - Probability | Probability | Mathematics

Supermartingales | Multiplicative cascades | Random environment | Hoeffding and Azuma’s inequality | Large deviation inequality | Martingale differences | Exponential inequality | Directed polymers | Convergence rate | Bernstein’s inequality | Concentration inequality | Free energy | Hoeffding and Azuma's inequality | Bernstein's inequality | STATISTICS & PROBABILITY | STRONG DISORDER | ITERATED RANDOM MULTIPLICATIONS | DIFFUSION | INVARIANT DISTRIBUTIONS | LARGE DEVIATIONS | Martingale differences Supermartingales Large deviation inequality Exponential inequality Bernstein's inequality Hoeffding and Azuma's inequality Directed polymers Random environment Concentration inequality Free energy Convergence rate Multiplicative cascades | Polymers | Analysis | Mathematics - Probability | Probability | Mathematics

Journal Article

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