ﻻ يوجد ملخص باللغة العربية
We study the asymptotic behaviour of once-reinforced biased random walk (ORbRW) on Galton-Watson trees. Here the underlying (unreinforced) random walk has a bias towards or away from the root. We prove that in the setting of multiplicative once-reinforcement the ORbRW can be recurrent even when the underlying biased random walk is ballistic. We also prove that, on Galton-Watson trees without leaves, the speed is positive in the transient regime. Finally, we prove that, on regular trees, the speed of the ORbRW is monotone decreasing in the reinforcement parameter when the underlying random walk has high speed, and the reinforcement parameter is small.
We revisit an unpublished paper of Vervoort (2002) on the once reinforced random walk, and prove that this process is recurrent on any graph of the form $mathbb{Z}times Gamma$, with $Gamma$ a finite graph, for sufficiently large reinforcement paramet
We study a biased random walk on the interlacement set of $mathbb{Z}^d$ for $dgeq 3$. Although the walk is always transient, we can show, in the case $d=3$, that for any value of the bias the walk has a zero limiting speed and actually moves slower than any power.
We study the evolution of a random walker on a conservative dynamic random environment composed of independent particles performing simple symmetric random walks, generalizing results of [16] to higher dimensions and more general transition kernels w
We consider a random walker in a dynamic random environment given by a system of independent simple symmetric random walks. We obtain ballisticity results under two types of perturbations: low particle density, and strong local drift on particles. Su
The Maki-Thompson rumor model is defined by assuming that a population represented by a graph is subdivided into three classes of individuals; namely, ignorants, spreaders and stiflers. A spreader tells the rumor to any of its nearest ignorant neighb