Related papers: Expectation values in the random walk theory and t…
All statistical information about the heat can be obtained with the probability distribution of the heat functional. This paper derives analytically the expression for the distribution of the heat, through path integral, for a diffusive…
In this paper random walks on the Penrose lattice are investigated. Heat kernel estimates and the invariance principle are shown.
We consider time-dependent random walks among time-dependent conductances. For discrete time random walks, we show that, unlike the time-independent case, two-sided Gaussian heat kernel estimates are not stable under perturbations. This is…
We will investigate a random mass splitting model and the closely related random walk in a random environment (RWRE). The heat kernel for the RWRE at time t is the mass splitting distribution at t. We prove a quenched invariance principle…
The general relationship between an arbitrary frequency distribution and the expectation value of the frequency distributions of its samples is esablished. A set of combinations of expectation values whose value does not in general depend…
Via a Dirichlet form extension theorem and making full use of two-sided heat kernel estimates, we establish quenched invariance principles for random walks in random environments with a boundary. In particular, we prove that the random walk…
We consider reversible random walks in random environment obtained from symmetric long--range jump rates on a random point process. We prove almost sure transience and recurrence results under suitable assumptions on the point process and…
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 $\alpha>d$,…
Random walk is a fundamental concept with applications ranging from quantum physics to econometrics. Remarkably, one specific model of random walks appears to be ubiquitous across many fields as a tool to analyze transport phenomena in…
Random walks provide a simple conventional model to describe various transport processes, for example propagation of heat or diffusion of matter through a medium. However, in many practical cases the medium is highly irregular due to…
In this paper necessary and sufficient conditions are presented for heat kernel upper bounds for random walks on weighted graphs. Several equivalent conditions are given in the form of isoperimetric inequalities.
Propagation in quantum walks is revisited by showing that very general 1D discrete-time quantum walks with time- and space-dependent coefficients can be described, at the continuous limit, by Dirac fermions coupled to electromagnetic…
Diffusion mediated reaction models are particularly ubiquitous in the description of physical, chemical or biological processes. The random walk schema is a useful tool for formulating these models. Recently, evanescent random walk models…
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…
In this paper, we derive upper bounds for the heat kernel of the simple random walk on the infinite cluster of a supercritical long range percolation process. For any $d \geq 1$ and for any exponent $s \in (d, (d+2) \wedge 2d)$ giving the…
We consider on-diagonal heat kernel estimates and the laws of the iterated logarithms for a switch-walk-switch random walk on a lamplighter graph under the condition that the random walk on the underlying graph enjoys sub-Gaussian heat…
There has recently been considerable interest in quantum walks in connection with quantum computing. The walk can be considered as a quantum version of the so-called correlated random walk. We clarify a strong structural similarity between…
The diffusion equation and its time-fractional counterpart can be obtained via the diffusion limit of continuous-time random walks with exponential and heavy-tailed waiting time distributions. The space dependent variable-order…
In this paper we consider a time-continuous random walk in $\mathbb{Z}^d$ in a dynamical random environment with symmetric jump rates to nearest neighbours. We assume that these random conductances are stationary and ergodic and, moreover,…
A fractional reaction-diffusion equation is derived from a continuous time random walk model when the transport is dispersive. The exit from the encounter distance, which is described by the algebraic waiting time distribution of jump…