Related papers: Noise stability on hyperbolic groups

We address nonautonomous initial boundary value problems for decoupled linear first-order one-dimensional hyperbolic systems, investigating the phenomenon of finite time stabilization. We establish sufficient and necessary conditions…

We obtain sharp estimates on the growth rate of stable commutator length on random (geodesic) words, and on random walks, in hyperbolic groups and groups acting nondegenerately on hyperbolic spaces. In either case, we show that with high…

We construct an uncountable sequence of groups acting uniformly properly on hyperbolic spaces. We show that only countably many of these groups can be virtually torsion-free. This gives new examples of groups acting uniformly properly on…

We provide a unified geometrical description for analyzing the stability of holonomic quantum gates in the presence of imprecise driving controls (parametric noise). We consider the situation in which these fluctuations do not affect the…

We consider admissible random walks on hyperbolic graphs. For a given harmonic function on such a graph, we prove that asymptotic properties of non-tangential boundedness and non-tangential convergence are almost everywhere equivalent. The…

We investigate the finite time stability property of one-dimensional nonautonomous initial boundary value problems for linear decoupled hyperbolic systems with nonlinear boundary conditions. We establish sufficient and necessary conditions…

We consider non-degenerate, finitely supported random walks on a free group. We show that the entropy and the linear drift vary analytically with th eprobability of constant support.

We study the asymptotic distribution of random walks on $\mathbb Z^d$ ($d\ge1$) in deterministic reversible environments defined by an assignment of a positive conductance to each edge of $\mathbb Z^d$. We identify a deterministic set of…

In this paper we consider finitary symmetric random walks on groups. We construct new possible asymptotics for the drift. We show that the drift can be very close to linear ant yet sublinear. We also give estimates for entropy growth of…

When two synchronised phase oscillators are perturbed by weak noise, they display occasional losses of synchrony, called phase slips. The slips can be characterised by their location in phase space and their duration. We show that when…

Let $\Gamma$ be a relatively hyperbolic group and let $\mu$ be an admissible symmetric finitely supported probability measure on $\Gamma$. We extend Floyd-Ancona type inequalities up to the spectral radius of $\mu$. We then show that when…

We investigate some properties of the dynamical system of point vortices on the hyperboloid. This system has noncompact symmetry SL(2, R) and a coadjoint equivariant momentum map J. The relative equilibrium conditions are found and the…

We show that on every affine Weyl group natural random walks are noise sensitive in total variation.

We investigate the dynamics of continuous-time two-particle quantum walks on a one-dimensional noisy lattice. Depending on the initial condition, we show how the interplay between particle indistinguishability and interaction determines…

In this paper we consider the global stability of solutions of an affine stochastic differential equation. The differential equation is a perturbed version of a globally stable linear autonomous equation with unique zero equilibrium where…

We show that for each $\lambda \in [\frac{1}{2}, 1]$, there exists a solvable group and a finitely supported measure such that the associated random walk has upper speed exponent $\lambda$.

We study random walks on the isometry group of a Gromov hyperbolic space or Teichm\"uller space. We prove that the translation lengths of random isometries satisfy a central limit theorem if and only if the random walk has finite second…

We propose a general framework for quantum walks on d-dimensional spaces. We investigate asymptotic behavior of these walks. Among them, existence of limit distribution of homogeneous walks is proved. In this theorem, the support of the…

The usual random walk on a group (homogeneous both in time and in space) is determined by a probability measure on the group. In a random walk with random transition probabilities this single measure is replaced with a stationary sequence…

We present a probabilistic theory of random walks in turbid media with non-scattering regions. It is shown that important characteristics such as diffusion constants, average step lengths, crossing statistics and void spacings can be…