Non-homogeneous random walks with stochastic resetting: an application to the Gillis model

Characterization of stationary states in random walks with stochastic resetting.

It is known that introducing a stochastic resetting in a random-walk process can lead to the emergence of a stationary state. Here we study this point from a general perspective through the derivation and analysis of mesoscopic (continuous-time random walk) equations for both jump and velocity models with stochastic resetting. In the case of jump models it is shown that stationary states emerge...

Homogeneous Superpixels from Random Walks

This paper presents a novel algorithm to generate homogeneous superpixels from the process of Markov random walks. We exploit Markov clustering (MCL) as the methodology, a generic graph clustering method based on stochastic flow circulation. In particular, we introduce a new graph pruning strategy called compact pruning in order to capture intrinsic local image structure, and thereby keep the s...

Convergence of Cyclic Random Walks with an Application to Cryptanalysis

Imagine that you and some friends are playing a version of roulette. The wheel is divided into 36 sectors, alternately colored red and black. Before spinning the wheel, the contestant chooses a color and then wins or loses depending on whether or not his color comes up. You, the master player, have honed an ability to spin the wheel exactly 3620◦ with high probability. Thus, if the wheel is ini...

Zariski Dense Random Walks on Homogeneous Spaces

Anisotropic Branching Random Walks on Homogeneous Trees

Symmetric branching random walk on a homogeneous tree exhibits a weak survival phase: For parameter values in a certain interval, the population survives forever with positive probability, but, with probability one, eventually vacates every finite subset of the tree. In this phase, particle trails must converge to the geometric boundary of the tree. The random subset 3 of the boundary consisti...