Related papers: Invariance principle and local limit theorem for a…
We establish the quenched local limit theorem for reversible random walk on $\Z^d$ (with $d\ge 2$) among stationary ergodic random conductances that permit jumps of arbitrary length. The proof is based on the weak parabolic Harnack…
We study random walks on $\mathbb Z^d$ (with $d\ge 2$) among stationary ergodic random conductances $\{C_{x,y}\colon x,y\in\mathbb Z^d\}$ that permit jumps of arbitrary length. Our focus is on the Quenched Invariance Principle (QIP) which…
We study the quenched invariance principle for random conductance models with long range jumps on $\Z^d$, where the transition probability from $x$ to $y$ is, on average, comparable to $|x-y|^{-(d+\alpha)}$ with $\alpha\in (0,2)$ but is…
We study random walks on $\mathbb Z^d$ among random conductances $\{C_{xy}\colon x,y\in\mathbb Z^d\}$ that permit jumps of arbitrary length. Apart from joint ergodicity with respect to spatial shifts, we assume only that the…
We study variable-speed random walks on $\mathbb Z$ driven by a family of nearest-neighbor time-dependent random conductances $\{a_t(x,x+1)\colon x\in\mathbb Z, t\ge0\}$ whose law is assumed invariant and ergodic under space-time shifts. We…
We consider a random walk on a random graph $(V,E)$, where $V$ is the set of open sites under i.i.d. Bernoulli site percolation on the multi-dimensional integer set $\mathbf{Z}^d$, and the transition probabilities of the walk are generated…
We consider the random conductance model in a stationary and ergodic environment. Under suitable moment conditions on the conductances and their inverse, we prove a quenched invariance principle for the random walk among the random…
We consider a stationary and ergodic random field $\{\omega(e) : e \in E_d\}$ that is parameterized by the edge set of the Euclidean lattice $\mathbb{Z}^d$, $d \geq 2$. The random variable $\omega(e)$, taking values in $[0, \infty)$ and…
We study a continuous time random walk X in an environment of dynamic random conductances. We assume that the conductances are stationary ergodic, uniformly bounded and bounded away from zero and polynomially mixing in space and time. We…
We study a one-dimensional random walk among random conductances, with unbounded jumps. Assuming the ergodicity of the collection of conductances and a few other technical conditions (uniform ellipticity and polynomial bounds on the tails…
We study a class of non-reversible, continuous-time random walks in random environments on $\mathbb{Z}^d$ that admit a cycle representation with finite cycle length. The law of the transition rates, taking values in $[0, \infty)$, is…
We establish a quenched local central limit theorem for the dynamic random conductance model on $\mathbb{Z}^d$ only assuming ergodicity with respect to space-time shifts and a moment condition. As a key analytic ingredient we show H\"older…
We study a continuous time random walk, $X$, on ${\mathbb{Z}}^d$ in an environment of random conductances taking values in $(0,\infty)$. We assume that the law of the conductances is ergodic with respect to space shifts. We prove a quenched…
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 study a one-dimensional random walk among random conductances, with unbounded jumps. Assuming the ergodicity of the collection of conductances and a few other technical conditions (uniform ellipticity and polynomial bounds on the tails…
We derive a quenched invariance principle for random walks in random environments whose transition probabilities are defined in terms of weighted cycles of bounded length. To this end, we adapt the proof for random walks among random…
We study a one-dimensional random walk among random conductances, with unbounded jumps. Assuming the ergodicity of the collection of conductances and a few other technical conditions (uniform ellipticity and polynomial bounds on the tails…
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 prove a quenched invariance principle for a class of random walks in random environment on $\mathbb{Z}^d$, where the walker alters its own environment. The environment consists of an outgoing edge from each vertex. The walker updates the…
We study a continuous time random walk $X$ in an environment of i.i.d. random conductances $\mu_e\in[1,\infty)$. We obtain heat kernel bounds and prove a quenched invariance principle for $X$. This holds even when…