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Contributions to the study of random walks in random environments
Random walks in random environment have raised a great interest in the last few years, both among applied scientists, notably as a way to refine models by taking... -
On countably skewed Brownian motion with accumulation point.
In this work we connect the theory of Dirichlet forms and direct stochastic calculus to obtain strong existence and pathwise uniqueness for Brownian motion that is... -
Martingale defocusing and transience of a self-interacting random walk
Suppose that $(X,Y,Z)$ is a random walk in $\Z^3$ that moves in the following way: on the first visit to a vertex only $Z$ changes by $\pm 1$ equally likely, while on... -
Transience of edge-reinforced random walk
We show transience of the edge-reinforced random walk for small reinforcement in dimension $d\ge3$. The argument adapts the proof of quasi-diffusive behaviour of the...
