Revista Matematica Iberoamericana, ISSN 0213-2230, 2016, Volume 32, Issue 2, pp. 511 - 532

We compute the exponential decay of the probability that a given multi-dimensional random walk stays in a convex cone up to time n, as n goes to infinity. We...

Cones | Laplace transform | Random walk | Exit time | MATHEMATICS | exit time | cones

Cones | Laplace transform | Random walk | Exit time | MATHEMATICS | exit time | cones

Journal Article

Inventiones mathematicae, ISSN 0020-9910, 10/2012, Volume 190, Issue 1, pp. 57 - 118

Let (ρ λ ) λ∈Λ be a holomorphic family of representations of a finitely generated group G into PSL(2,ℂ), parameterized by a complex manifold Λ. We define a...

Mathematics, general | Mathematics | MATHEMATICS | PRODUCTS | DYNAMICS | SUBGROUPS | RATIONAL MAPS | QUASI-CONFORMAL HOMEOMORPHISMS | RANDOM MATRICES | Geometric Topology | Complex Variables | Dynamical Systems

Mathematics, general | Mathematics | MATHEMATICS | PRODUCTS | DYNAMICS | SUBGROUPS | RATIONAL MAPS | QUASI-CONFORMAL HOMEOMORPHISMS | RANDOM MATRICES | Geometric Topology | Complex Variables | Dynamical Systems

Journal Article

2006, Lecture notes in mathematics, ISBN 9783540330271, Volume 1885., vii, 195

Book

Selecta Mathematica, ISSN 1022-1824, 4/2018, Volume 24, Issue 2, pp. 751 - 874

We consider a fully inhomogeneous stochastic higher spin six vertex model in a quadrant. For this model we derive concise integral representations for...

Secondary 05E05 | Mathematics, general | Mathematics | Primary 60K35 | 82B23 | ORTHOGONAL POLYNOMIAL ENSEMBLES | MATHEMATICS | YANG-BAXTER EQUATION | MATHEMATICS, APPLIED | RANDOM-WALKS | DYNAMICS | DUALITY | SYSTEMS

Secondary 05E05 | Mathematics, general | Mathematics | Primary 60K35 | 82B23 | ORTHOGONAL POLYNOMIAL ENSEMBLES | MATHEMATICS | YANG-BAXTER EQUATION | MATHEMATICS, APPLIED | RANDOM-WALKS | DYNAMICS | DUALITY | SYSTEMS

Journal Article

Ergodic Theory and Dynamical Systems, ISSN 0143-3857, 08/2017, Volume 37, Issue 5, pp. 1480 - 1491

We consider general transformations of random walks on groups determined by Markov stopping times and prove that the asymptotic entropy (respectively, rate of...

MATHEMATICS | MATHEMATICS, APPLIED | DISCRETE-GROUPS | SPACES | GROWTH | BOUNDARY | FORMULA | Asymptotic properties | Analogue | Random walk | Markov processes | Random walk theory | Entropy | Ergodic processes

MATHEMATICS | MATHEMATICS, APPLIED | DISCRETE-GROUPS | SPACES | GROWTH | BOUNDARY | FORMULA | Asymptotic properties | Analogue | Random walk | Markov processes | Random walk theory | Entropy | Ergodic processes

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 12/2019, Volume 480, Issue 1, p. 123360

A probabilistic approach is provided to establish new hypergeometric identities. It is based on the calculation of moments of the limiting distribution of the...

Generalized hypergeometric series | Elephant random walk | MATHEMATICS | MATHEMATICS, APPLIED

Generalized hypergeometric series | Elephant random walk | MATHEMATICS | MATHEMATICS, APPLIED

Journal Article

Annals of Probability, ISSN 0091-1798, 2018, Volume 46, Issue 4, pp. 1807 - 1877

Consider a Markov chain (X-n)(n >= 0) with values in the state space X. Let f be a real function on X and set S-n = Sigma(n)(i=1) f(X-i), n >= 1. Let P-x be...

Markov chain | Random walk | Harmonic function | Exit time | Limit theorem | AFFINE RANDOM-WALKS | exit time | STATISTICS & PROBABILITY | harmonic function | POTENTIAL-THEORY | CONICAL DOMAINS | limit theorem | ASYMPTOTIC-BEHAVIOR | DISTRIBUTIONS | random walk | 1ST-PASSAGE TIMES | ORDERED RANDOM-WALKS | CONVERGENCE | CHAINS | STABLE LAWS | Probability | Mathematics

Markov chain | Random walk | Harmonic function | Exit time | Limit theorem | AFFINE RANDOM-WALKS | exit time | STATISTICS & PROBABILITY | harmonic function | POTENTIAL-THEORY | CONICAL DOMAINS | limit theorem | ASYMPTOTIC-BEHAVIOR | DISTRIBUTIONS | random walk | 1ST-PASSAGE TIMES | ORDERED RANDOM-WALKS | CONVERGENCE | CHAINS | STABLE LAWS | Probability | Mathematics

Journal Article

Canadian Journal of Mathematics, ISSN 0008-414X, 2012, Volume 64, Issue 5, pp. 961 - 990

We study the densities of uniform random walks in the plane. A special focus is on the case of short walks with three or four steps and, less completely, those...

Hypergeometric functions | Random walks | Mahler measure | INTEGRALS | MATHEMATICS | random walks | hypergeometric functions | ASYMPTOTICS | MAHLER MEASURES | INSTABILITY ZONES

Hypergeometric functions | Random walks | Mahler measure | INTEGRALS | MATHEMATICS | random walks | hypergeometric functions | ASYMPTOTICS | MAHLER MEASURES | INSTABILITY ZONES

Journal Article

Journal of Statistical Physics, ISSN 0022-4715, 4/2017, Volume 167, Issue 2, pp. 173 - 204

We consider an open quantum walk on a graph, and the random variables defined as the passage time and number of visits at a given point of the graph. We study...

Quantum trajectories | Quantum Markov chains | Physical Chemistry | Theoretical, Mathematical and Computational Physics | Open quantum walks | Completely positive maps | Quantum Physics | Physics | Statistical Physics and Dynamical Systems | ALGEBRAS | SYMMETRICAL MARKOV SEMIGROUPS | RECURRENCE | PHYSICS, MATHEMATICAL | OPERATORS | Markov processes

Quantum trajectories | Quantum Markov chains | Physical Chemistry | Theoretical, Mathematical and Computational Physics | Open quantum walks | Completely positive maps | Quantum Physics | Physics | Statistical Physics and Dynamical Systems | ALGEBRAS | SYMMETRICAL MARKOV SEMIGROUPS | RECURRENCE | PHYSICS, MATHEMATICAL | OPERATORS | Markov processes

Journal Article

Groups, Geometry, and Dynamics, ISSN 1661-7207, 2013, Volume 7, Issue 4, pp. 791 - 820

We study some spectral properties of random walks on infinite countable amenable groups with an emphasis on locally finite groups, e. g. the infinite symmetric...

Return probability | Spectral distribution | Locally finite group | Isospectral profile | Random walk | Ultra-metric space | Köhlbeckertransform | Infinite divisible distribution | Laplace transform | Legendre transform | infinite divisible distribution | INEQUALITIES | ABELIAN-GROUPS | ultra-metric space | Kohlbecker transform | MATHEMATICS | return probability | spectral distribution | isospectral profile | TRANSIENCE | PROFILE | ULTRACONTRACTIVITY | RECURRENCE | locally finite group | OPERATORS | RIEMANNIAN-MANIFOLDS

Return probability | Spectral distribution | Locally finite group | Isospectral profile | Random walk | Ultra-metric space | Köhlbeckertransform | Infinite divisible distribution | Laplace transform | Legendre transform | infinite divisible distribution | INEQUALITIES | ABELIAN-GROUPS | ultra-metric space | Kohlbecker transform | MATHEMATICS | return probability | spectral distribution | isospectral profile | TRANSIENCE | PROFILE | ULTRACONTRACTIVITY | RECURRENCE | locally finite group | OPERATORS | RIEMANNIAN-MANIFOLDS

Journal Article

Ergodic Theory and Dynamical Systems, ISSN 0143-3857, 02/2019, Volume 39, Issue 2, pp. 474 - 499

We show the exact dimensionality of harmonic measures associated with random walks on groups acting on a hyperbolic space under a finite first moment...

HAUSDORFF DIMENSION | MATHEMATICS | MATHEMATICS, APPLIED | RANDOM-WALKS | EMBEDDINGS | BOUNDARY | DRIFT | ENTROPY | Riemann manifold | Random walk

HAUSDORFF DIMENSION | MATHEMATICS | MATHEMATICS, APPLIED | RANDOM-WALKS | EMBEDDINGS | BOUNDARY | DRIFT | ENTROPY | Riemann manifold | Random walk

Journal Article

Annals of Probability, ISSN 0091-1798, 01/2018, Volume 46, Issue 1, pp. 302 - 336

We study a continuous-time random walk, X, on Z(d) in an environment of dynamic random conductances taking values in (0,infinity). We assume that the law of...

Moser iteration | Random walk | Time dependent dynamics | random walk | LIMIT-THEOREMS | STATISTICS & PROBABILITY | RANDOM CONDUCTANCE MODEL | HOMOGENIZATION | RANDOM ENVIRONMENT | Mathematics - Probability | Probability | Mathematics

Moser iteration | Random walk | Time dependent dynamics | random walk | LIMIT-THEOREMS | STATISTICS & PROBABILITY | RANDOM CONDUCTANCE MODEL | HOMOGENIZATION | RANDOM ENVIRONMENT | Mathematics - Probability | Probability | Mathematics

Journal Article

2008, 1st ed., ISBN 0375424040, xi, 252

Book

The Annals of Probability, ISSN 0091-1798, 9/2013, Volume 41, Issue 5, pp. 3582 - 3605

We consider nondegenerate, finitely supported random walks on a finitely generated Gromov hyperbolic group. We show that the entropy and the escape rate are...

Mathematical theorems | Infinity | Symbolism | Random walk | Mathematical constants | Entropy | Mathematical functions | Matrices | Continuous functions | Hyperbolic group | hyperbolic group | STATISTICS & PROBABILITY | Probability | Mathematics | 60B15 | 60G50

Mathematical theorems | Infinity | Symbolism | Random walk | Mathematical constants | Entropy | Mathematical functions | Matrices | Continuous functions | Hyperbolic group | hyperbolic group | STATISTICS & PROBABILITY | Probability | Mathematics | 60B15 | 60G50

Journal Article

Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, 04/2016, Volume 49, Issue 20, p. 205003

J. Phys. A 49, 205003 (2016) We investigate statistics of lead changes of the maxima of two discrete-time random walks in one dimension. We show that the...

Levy flights | random walks | statistics of maxima | Probability | Condensed Matter | Mathematics | Statistical Mechanics | Mathematical Physics | Physics | MATHEMATICS AND COMPUTING

Levy flights | random walks | statistics of maxima | Probability | Condensed Matter | Mathematics | Statistical Mechanics | Mathematical Physics | Physics | MATHEMATICS AND COMPUTING

Journal Article

ISSN 0091-1798, 2018

Journal Article

Advances in Mathematics, ISSN 0001-8708, 04/2019, Volume 347, pp. 739 - 779

We provide a unified framework to compute the stationary distribution of any finite irreducible Markov chain or equivalently of any irreducible random walk on...

McCammond expansion | Semaphore codes | Markov chains | Stationary distributions | Karnofsky–Rhodes expansion | Tsetlin library | MATHEMATICS | Karnofsky-Rhodes expansion | RANDOM-WALKS | Markov processes | Analysis | Algebra

McCammond expansion | Semaphore codes | Markov chains | Stationary distributions | Karnofsky–Rhodes expansion | Tsetlin library | MATHEMATICS | Karnofsky-Rhodes expansion | RANDOM-WALKS | Markov processes | Analysis | Algebra

Journal Article

2006, 1st ed., ISBN 9780817643652, xx, 352

Stochastic processes | Distribution (Probability theory) | Statistics for Business/Economics/Mathematical Finance/Insurance | Statistics for Life Sciences, Medicine, Health Sciences | Probability Theory and Stochastic Processes | Statistical Theory and Methods | Mathematics | Statistics for Engineering, Physics, Computer Science, Chemistry & Geosciences | Applications of Mathematics

Book

2011, 2nd ed., ISBN 9781439818824, xxiv, 466

"The second edition of a bestseller, this textbook delineates stochastic processes, emphasizing applications in biology. It includes MATLAB throughout the book...

Stochastic processes | Biomathematics

Stochastic processes | Biomathematics

Book

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