Related papers: A local central limit theorem for random walks on …

We establish and generalise several bounds for various random walk quantities including the mixing time and the maximum hitting time. Unlike previous analyses, our derivations are based on rather intuitive notions of local expansion…

We prove a central limit theorem for a certain class of functions on sparse rank-one inhomogeneous random graphs endowed with additional i.i.d. edge and vertex weights. Our proof of the central limit theorem uses a perturbative form of…

Let ${\cal T}$ be a rooted Galton-Watson tree with offspring distribution $\{p_k\}$ that has $p_0=0$, mean $m=\sum kp_k>1$ and exponential tails. Consider the $\lambda$-biased random walk $\{X_n\}_{n\geq 0}$ on ${\cal T}$; this is the…

Random walks cannot, in general, be pushed forward by quasi-isometries. Tame Markov chains were introduced as a `quasi-isometry invariant' are a generalization of random walks. In this paper, we construct several examples of tame Markov…

We prove quenched versions of (i) a large deviations principle (LDP), (ii) a central limit theorem (CLT), and (iii) a local central limit theorem (LCLT) for non-autonomous dynamical systems. A key advance is the extension of the spectral…

We study the asymptotic behavior of a nonlattice random walk in a general cone of $R^d$ . Following the approach initiated by D. Denisov and V. Wachtel in [8], we use a strong approximation of random walks by the Brownian motion and prove…

We consider random walks in dynamic random environments which arise naturally as spatial embeddings of ancestral lineages in spatial locally regulated population models. In particular, as the main result, we prove the quenched central limit…

We consider transient random walks on a strip in a random environment. The model was introduced by Bolthausen and Goldsheid [Comm. Math. Phys. 214 (2000) 429--447]. We derive a strong law of large numbers for the random walks in a general…

We prove a Chernoff-type bound for sums of matrix-valued random variables sampled via a regular (aperiodic and irreducible) finite Markov chain. Specially, consider a random walk on a regular Markov chain and a Hermitian matrix-valued…

In this article we consider transient random walks on HNN extensions of finitely generated groups. We prove that the rate of escape w.r.t. some generalised word length exists. Moreover, a central limit theorem with respect to the…

We prove that the spectral radius of a strongly irreducible random walk on GLd(R) (or more generally the vector of moduli of eigenvalues of a Zariski-dense random walk on a reductive group) satisfies a central limit theorem under an order…

In this paper we consider the field of local times of a discrete-time Markov chain on a general state space, and obtain uniform (in time) upper bounds on the total variation distance between this field and the one of a sequence of $n$…

We establish scaling limits for the random walk whose state space is the range of a simple random walk on the four-dimensional integer lattice. These concern the asymptotic behaviour of the graph distance from the origin and the spatial…

For the perimeter length and the area of the convex hull of the first $n$ steps of a planar random walk, we study $n \to \infty$ mean and variance asymptotics and establish non-Gaussian distributional limits. Our results apply to random…

We show bounds on total variation and $L^{\infty}$ mixing times, spectral gap and magnitudes of the complex valued eigenvalues of a general (non-reversible non-lazy) Markov chain with a minor expansion property. This leads to the first…

We consider a multidimensional random walk in a product random environment with bounded steps, transience in some spatial direction, and high enough moments on the regeneration time. We prove an invariance principle, or functional central…

Completing a strategy of Gou\"ezel and Lalley, we prove a local limit theorem for the random walk generated by any symmetric finitely supported probability measure on a non-elementary Gromov-hyperbolic group: denoting by $R$ the inverse of…

We study a limit behavior of a sequence of Markov processes (or Markov chains) such that their distributions outside of any neighborhood of a "singular" point attract to some probability law. In any neighborhood of this point the behavior…

In this work we aim at proving central limit theorems for open quantum walks on $\mathbb{Z}^d$. We study the case when there are various classes of vertices in the network. Furthermore, we investigate two ways of distributing the vertex…

We define the local empirical process, based on $n$ i.i.d. random vectors in dimension $d$, in the neighborhood of the boundary of a fixed set. Under natural conditions on the shrinking neighborhood, we show that, for these local empirical…