Related papers: Noise sensitivity of random walks on groups

Using the technique of evolving sets, we explore the connection between entropy growth and transience for simple random walks on connected infinite graphs with bounded degree. In particular we show that for a simple random walk starting at…

We introduce an original way to estimate the memory parameter of the elephant random walk, a fascinating discrete time random walk on integers having a complete memory of its entire history. Our estimator is nothing more than a…

We study the discrete quantum groups $\Gamma$ whose group algebra has an inner faithful representation of type $\pi:C^*(\Gamma)\to M_K(\mathbb C)$. Such a representation can be thought of as coming from an embedding $\Gamma\subset U_K$. Our…

We research adaptive maximum likelihood-type estimation for an ergodic diffusion process where the observation is contaminated by noise. This methodology leads to the asymptotic independence of the estimators for the variance of observation…

The effect of unitary noise on the discrete one-dimensional quantum walk is studied using computer simulations. For the noiseless quantum walk, starting at the origin (n=0) at time t=0, the position distribution Pt(n) at time t is very…

The sensitivity of quantum systems to external disturbances is a fundamental problem for the implementation of functional quantum devices, quantum information and computation. Based on remarkable experimental progress in optics and…

When the memory parameter of the elephant random walk is above a critical threshold, the process becomes superdiffusive and, once suitably normalised, converges to a non-Gaussian random variable. In a recent paper by the three first…

We extend some properties of random walks on hyperbolic groups to random walks on convergence groups. In particular we prove that if a convergence group $G$ acts on a compact metrizable space $M$ with the convergence property then we can…

We explore static noise in a discrete quantum random walk over a homogeneous cyclic graph, focusing on spectral and dynamical properties. Using a three-parameter unitary coin, we control the spectral structure of the noiseless step operator…

Partial differential equations with random inputs have become popular models to characterize physical systems with uncertainty coming from, e.g., imprecise measurement and intrinsic randomness. In this paper, we perform asymptotic rare…

We study using large deviation theory the fluctuations of time-integrated functionals or observables of the unbiased random walk evolving on Erd\"os-R\'enyi random graphs, and construct a modified, biased random walk that explains how these…

We study the problem of detecting a random walk on a graph from a sequence of noisy measurements at every node. There are two hypotheses: either every observation is just meaningless zero-mean Gaussian noise, or at each time step exactly…

In animal groups, individual decisions are best characterised by probabilistic rules. Furthermore, animals of many species live in small groups. Probabilistic interactions among small numbers of individuals lead to a so called intrinsic…

We generalize the Metropolis et al. random walk algorithm to the situation where the energy is noisy and can only be estimated. Two possible applications are for long range potentials and for mixed quantum-classical simulations. If the…

We consider the simple random walk on the infinite cluster of a general class of percolation models on $\mathbb{Z}^d$, $d\geq 3$, including Bernoulli percolation as well as models with strong, algebraically decaying correlations. For almost…

We study the random walk on a finite dihedral group $G$ driven by the uniform measure on $k$ independently and uniformly chosen elements. We show that the walk exhibits cutoff with high probability throughout nearly the entire regime $1 \ll…

We show that in a broad class of processes that show a $1/f^{\alpha}$ spectrum, the power also explicitly depends on the characteristic time scale. Despite an enormous amount of work, this generic behavior remains so far overlooked and…

Random walks represent an important tool for probing the structural and dynamical properties of networks and modeling transport and diffusion processes on networks. However, when individuals' movement becomes dictated by more complicated…

We show that on groups generated by bounded activity automata, every symmetric, finitely supported probability measure has the Liouville property. More generally we show this for every group of automorphisms of bounded type of a rooted…

We show that a random walk on the mapping class group of an orientable surface gives rise to a pseudo-Anosov element with asymptotic probability one. Our methods apply to many subgroups of the mapping class group, including the Torelli…