The laws of Chung and Hirsch for Cauchy's principal values related to Brownian local times.
Invariance principles for ranked excursion lengths and heights.
On the increments of the principal value of Brownian local time.
A note on directed polymers in Gaussian environments.
Aldous’ conjecture on a killed branching random walk
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 speed is zero....
A family of integral representations for the brownian variables
Shortest excursion lengths
Universality in Sherrington–Kirkpatrick's spin glass model
The spread of a catalytic branching random walk
We consider a catalytic branching random walk on that branches at the origin only. In the supercritical regime we establish a law of large number for the maximal position : For some constant , almost surely on the set of infinite number of visits of the origin. Then we determine all possible limiting laws for as goes to infinity.
Penalization of the Wiener measure and principal values
Asymptotics for the survival probability in a killed branching random walk
Consider a discrete-time one-dimensional supercritical branching random walk. We study the probability that there exists an infinite ray in the branching random walk that always lies above the line of slope − , where denotes the asymptotic speed of the right-most position in the branching random walk. Under mild general assumptions upon the distribution of the branching random walk, we prove that when → 0, this probability decays like exp{−(+o(1)) / 1/2}, where is a positive constant depending...
Einstein relation for biased random walk on Galton–Watson trees
We prove the Einstein relation, relating the velocity under a small perturbation to the diffusivity in equilibrium, for certain biased random walks on Galton–Watson trees. This provides the first example where the Einstein relation is proved for motion in random media with arbitrarily slow traps.
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