arXiv subjects

Marina Vachkovskaia

Publications and source records attributed to Marina Vachkovskaia.

20 records · Page 2Linked to original sources

arXiv2006

Percolation for the stable marriage of Poisson and Lebesgue

Let $Ξ$ be the set of points (we call the elements of $Ξ$ centers) of Poisson process in $\R^d$, $d\geq 2$, with unit intensity. Consider the allocation of $\R^d$ to $Ξ$ which is stable in the sense of Gale-Shapley marriage problem and in which each center claims a region of volume $α\leq 1$. We prove that there is no percolation in the set of claimed sites if $α$ is small enough, and that, for high dimensions, there is percolation in the set of claimed sites if $α<1$ is large enough.

math.PR↗

arXiv2005

Random walk attracted by percolation clusters

Starting with a percolation model in $\Z^d$ in the subcritical regime, we consider a random walk described as follows: the probability of transition from $x$ to $y$ is proportional to some function $f$ of the size of the cluster of $y$. This function is supposed to be increasing, so that the random walk is attracted by bigger clusters. For $f(t)=e^{βt}$ we prove that there is a phase transition in $β$, i.e., the random walk is subdiffusive for large $β$ and is diffusive for small $β$.

math.PR↗