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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
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
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
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
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
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
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
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
Journal Article
Groups, Geometry, and Dynamics, ISSN 1661-7207, 2013, Volume 7, Issue 4, pp. 791 - 820
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
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
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
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
Journal Article
2005, 2nd ed., ISBN 981256361X, xvi, 380
Book
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
Journal Article
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
Book
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