We ascertain the diffusively scaled limit of a periodic Lorentz process in a strip with an almost reflecting wall at the origin. Here, almost reflecting means that the wall contains a small hole… (More)

In the proof of the invariance principle for locally perturbed periodic Lorentz process with finite horizon, a lot of delicate results were needed concerning the recurrence properties of its… (More)

In the classical paper of Dvoretzky-Erdős [4], asymptotics for the expected value and the variance of the number of distinct sites visited by a Simple Symmetric Random Walk were calculated. Here,… (More)

We consider a long Lorentz tube with absorbing boundaries. Particles are injected to the tube from the left end. We compute the equilibrium density profiles in two cases: the semi-infinite tube (in… (More)

We calculate asymptotics for the expectation and the variance of the number of distinct sites visited by a Random Walk with Internal States. We adapt the argument of Dvoretzky and Erdős. For the two… (More)

We calculate asymptotics for the expectation and the variance of the number of distinct sites visited by a Random Walk with Internal States. We adapt the argument of Dvoretzky and Erdős. For the two… (More)

We prove that the local time process of a planar simple random walk, when time is scaled logarithmically, converges to a non-degenerate pure jump process. The convergence takes place in the Skorokhod… (More)