Random sums of random vectors and multitype families of productive individuals.
Random time changes for sock-sorting and other stochastic process limit theorems.
Random trigonometric polynomials with nonidentically distributed coefficients.
Random walk in a strongly inhomogeneous environment and invasion percolation
Random walk local time approximated by a brownian sheet combined with an independent brownian motion
Let ξ(k, n) be the local time of a simple symmetric random walk on the line. We give a strong approximation of the centered local time process ξ(k, n)−ξ(0, n) in terms of a brownian sheet and an independent Wiener process (brownian motion), time changed by an independent brownian local time. Some related results and consequences are also established.
Random walk on a discrete torus and random interlacements.
Random walk on graphs with regular resistance and volume growth
In this paper characterizations of graphs satisfying heat kernel estimates for a wide class of space–time scaling functions are given. The equivalence of the two-sided heat kernel estimate and the parabolic Harnack inequality is also shown via the equivalence of the upper (lower) heat kernel estimate to the parabolic mean value (and super mean value) inequality.
Random walk on periodic trees.
Random walk over a hypersphere.
Random walk probabilities in terms of Legendre polynomials
Random Walks and Trees
These notes provide an elementary and self-contained introduction to branching random walks. Section 1 gives a brief overview of Galton–Watson trees, whereas Section 2 presents the classical law of large numbers for branching random walks. These two short sections are not exactly indispensable, but they introduce the idea of using size-biased trees, thus giving motivations and an avant-goût to the main part, Section 3, where branching random walks...
Random walks in with non-zero drift absorbed at the axes
Spatially homogeneous random walks in with non-zero jump probabilities at distance at most , with non-zero drift in the interior of the quadrant and absorbed when reaching the axes are studied. Absorption probabilities generating functions are obtained and the asymptotic of absorption probabilities along the axes is made explicit. The asymptotic of the Green functions is computed along all different infinite paths of states, in particular along those approaching the axes.
Random walks in a quarter plane with zero drifts. I. Ergodicity and null recurrence
Random Walks in Attractive Potentials: The Case of Critical Drifts
We consider random walks in attractive potentials - sub-additive functions of their local times. An application of a drift to such random walks leads to a phase transition: If the drift is small than the walk is still sub-ballistic, whereas the walk is ballistic if the drift is strong enough. The set of sub-critical drifts is convex with non-empty interior and can be described in terms of Lyapunov exponents (Sznitman, Zerner ). Recently it was shown that super-critical drifts lead to a limiting...
Random walks in random medium on Z and Lyapunov spectrum
Random walks on a tree and capacity in the interval
Random Walks on Amalgams.
Random walks on an m-dimensional cube.
Random walks on finite groups and rapidly mixing Markov chains
Random walks on finite groups with few random generators.