Orthogonal polynomial ensembles in probability theory.
Eigenvalues of the Laguerre process as non-colliding squared Bessel processes.
Ordered random walks.
Non-colliding random walks, tandem queues, and discrete orthogonal polynomial ensembles.
Upper tails of self-intersection local times of random walks: survey of proof techniques
The asymptotics of the probability that the self-intersection local time of a random walk on 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 recently elaborated...
Large systems of path-repellent Brownian motions in a trap at positive temperature.
Potential confinement property of the parabolic Anderson model
We consider the parabolic Anderson model, the Cauchy problem for the heat equation with random potential in ℤ. We use i.i.d. potentials :ℤ→ℝ in the third universality class, namely the class of , in the classification of van der Hofstad, König and Mörters [ (2006) 307–353]. This class consists of potentials whose logarithmic moment generating function is regularly varying with parameter =1, but do not belong to the class of so-called double-exponentially distributed potentials studied...
Annealed deviations of random walk in random scenery
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