Related papers: Lyapunov exponents, shape theorems and large devia…
It is known that a one-dimensional quantum particle is localized when subjected to an arbitrarily weak random potential. It is conjectured that localization also occurs for an arbitrarily weak potential generated from the nonlinear…
The Lyapunov spectra of random U(1) extensions of expanding maps on the torus were investigated in our previous work [NW2015]. Using the result, we extend the recent spectral approach for quenched limit theorems for expanding maps…
Consider a long-range percolation model on $\mathbb{Z}^d$ where the probability that an edge $\{x,y\} \in \mathbb{Z}^d \times \mathbb{Z}^d$ is open is proportional to $\|x-y\|_2^{-d-\alpha}$ for some $\alpha >0$ and where $d > 3…
We study a continuous-time random walk, $X$, on $\mathbb{Z}^d$ in an environment of dynamic random conductances taking values in $(0, \infty)$. We assume that the law of the conductances is ergodic with respect to space-time shifts. We…
A correlated random walk approach to diffusion is applied to the disordered nonoverlapping Lorentz gas. By invoking the Lu-Torquato theory for chord-length distributions in random media [J. Chem. Phys. 98, 6472 (1993)], an analytic…
We consider simple random walks on Delaunay triangulations generated by point processes in $\mathbb{R}^d$. Under suitable assumptions on the point processes, we show that the random walk satisfies an almost sure (or quenched) invariance…
The sensitivity of trajectories over finite time intervals t to perturbations of the initial conditions can be associated with a finite-time Lyapunov exponent lambda, obtained from the elements M_{ij} of the stability matrix M. For globally…
Random transvections generate a walk on the space of symplectic forms on $\mathbf{F}_q^{2n}$. The main result is establishing cutoff for this Markov chain. After $n+c$ steps, the walk is close to uniform while before $n-c$, it is far from…
The parametric maximum likelihood estimation problem is addressed in the context of quantum walk theory for quantum walks on the lattice of integers. A coin action is presented, with the real parameter $\theta$ to be estimated identified…
We study the behavior of the random walk in a continuum independent long-range percolation model, in which two given vertices $x$ and $y$ are connected with probability that asymptotically behaves like $|x-y|^{-\alpha}$ with $\alpha>d$,…
We consider homogeneous open quantum random walks on a lattice with finite dimensional local Hilbert space and we study in particular the position process of the quantum trajectories of the walk. We prove that the properly rescaled position…
Consider a sequence of independent random isometries of Euclidean space with a previously fixed probability law. Apply these isometries successively to the origin and consider the sequence of random points that we obtain this way. We prove…
Recent progress in the understanding of quenched invariance principles (QIP) for a continuous-time random walk on $\mathbb{Z}^d$ in an environment of dynamical random conductances is reviewed and extended to the $1$-dimensional case. The…
We consider random walks perturbed at zero which behave like (possibly different) random walks with i.i.d. increments on each half lines and restarts at $0$ whenever they cross that point. We show that the perturbed random walk, after being…
We study branching random walks in random environment on the $d$-dimensional square lattice, $d \geq 1$. In this model, the environment has finite range dependence, and the population size cannot decrease. We prove limit theorems (laws of…
Two fundamental theorems by Spitzer/Erickson and Kesten/Maller on the fluctuation type (positive divergence, negative divergence or oscillation) of a real-valued random walk $(S_{n})_{n\ge 0}$ with iid increments $X_{1},X_{2},\ldots$ and…
We prove an almost sure invariance principle for a random walker among i.i.d. conductances in $\Z^d$, $d\geq 2$. We assume conductances are bounded from above but we dot require they are bounded from below.
We derive the weak limit theorem for a class of long range type quantum walks. To do it, we analyze spectral properties of a time evolution operator and prove that modified wave operators exist and are complete.
We consider the continuous-time random walk of a particle in a two-dimensional self-affine quenched random potential of Hurst exponent $H>0$. The corresponding master equation is studied via the strong disorder renormalization procedure…
In this article we continue the study of the quenched distributions of transient, one-dimensional random walks in a random environment. In a previous article we showed that while the quenched distributions of the hitting times do not…