Displaying similar documents to “Lipschitz percolation.”

Aldous’ conjecture on a killed branching random walk

Yueyun Hu (2010)

Actes des rencontres du CIRM

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Consider a branching random walk on the real line with an killing barrier at zero: starting from a nonnegative point, particles reproduce and move independently, but are killed when they touch the negative half-line. The population of the killed branching random walk dies out almost surely in both critical and subcritical cases, where by subcritical case we mean that the rightmost particle of the branching random walk without killing has a negative speed and by critical case when this...

Upper tails of self-intersection local times of random walks: survey of proof techniques

Wolfgang König (2010)

Actes des rencontres du CIRM

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The asymptotics of the probability that the self-intersection local time of a random walk on ℤ d exceeds its expectation by a large amount is a fascinating subject because of its relation to some models from Statistical Mechanics, to large-deviation theory and variational analysis and because of the variety of the effects that can be observed. However, the proof of the upper bound is notoriously difficult and requires various sophisticated techniques. We survey some heuristics and some...

Random Walks in Attractive Potentials: The Case of Critical Drifts

Dmitry Ioffe, Yvan Velenik (2010)

Actes des rencontres du CIRM

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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...