Related papers: The Einstein relation for random walks on graphs
On a connected finite graph, we propose an evolution of weights including Ollivier's Ricci flow as a special case. During the evolution process, on each edge, the speed of change of weight is exactly the difference between the Wasserstein…
Convergence rate analyses of random walk Metropolis-Hastings Markov chains on general state spaces have largely focused on establishing sufficient conditions for geometric ergodicity or on analysis of mixing times. Geometric ergodicity is a…
In this article we consider a natural class of random walks on free products of graphs, which arise as convex combinations of random walks on the single factors. From the works of Gilch [6,7] it is well-known that for these random walks the…
A quantum walk is the quantum analogue of a random walk. While it is relatively well understood how quantum walks can speed up random walk hitting times, it is a long-standing open question to what extent quantum walks can speed up the…
This paper concerns the long-term behaviour of a system of interacting random walks labeled by vertices of a finite graph. The model is reversible which allows to use the method of electric networks in the study. In addition, examples of…
Dynamic graphs have emerged as an appropriate model to capture the changing nature of many modern networks, such as peer-to-peer overlays and mobile ad hoc networks. Most of the recent research on dynamic networks has only addressed the…
We consider a random walk in random environment with random holding times, that is, the random walk jumping to one of its nearest neighbors with some transition probability after a random holding time. Both the transition probabilities and…
The validity of Einstein's fluctuation-dissipation relation is discussed in respect to the type of relaxation in an isothermal system. The first model, presuming isothermic fluctuations, leads to the Einstein formula. The second model…
A proof is provided of a strong law of large numbers for a one-dimensional random walk in a dynamic random environment given by a supercritical contact process in equilibrium. The proof is based on a coupling argument that traces the…
We study the escape probability problem in random walks over graphs. Given vertices, $s,t,$ and $p$, the problem asks for the probability that a random walk starting at $s$ will hit $t$ before hitting $p$. Such probabilities can be…
Let $G$ be a finitely generated group of polynomial volume growth equipped with a word-length $|\cdot|$. The goal of this paper is to develop techniques to study the behavior of random walks driven by symmetric measures $\mu$ such that, for…
For the study of cosmological backreacktion an avaragng procedure is required. In this work a covariant and gauge invariant averaging formalism for finite volumes will be developed. This averaging will be applied to the scalar parts of…
The Einstein evolution equations have been written in a number of symmetric hyperbolic forms when the gauge fields--the densitized lapse and the shift--are taken to be fixed functions of the coordinates. Extended systems of evolution…
The black hole area theorem suggests that classical general relativity is the thermodynamic limit of a quantum statistics. The degrees of freedom of the statistical theory cannot be the spacetime metric. We argue that the statistical theory…
The relativistic time dilatation effect and Einstein's second postulate of special relativity are used to analyse train/embankment thought expriments, both Einstein's original one, and an extension where observers on two trains moving at…
An excited random walk is a non-Markovian extension of the simple random walk, in which the walk's behavior at time $n$ is impacted by the path it has taken up to time $n$. The properties of an excited random walk are more difficult to…
Continuous-time quantum walks are natural tools for spatial search, where one searches for a marked vertex in a graph. Sometimes, the structure of the graph causes the walker to get trapped, such that the probability of finding the marked…
The purpose of this paper is to provide an exact formula for the second moment of the empirical correlation of two independent Gaussian random walks as well as implicit formulas for higher moments. The proofs are based on a symbolically…
We study an inverse problem on a finite connected graph G = (X, E), on whose vertices a conductivity {\gamma} is defined. Our data consists in a sequence of partial observations of a fractional random walk on G. The observations are partial…
We consider a particle moving with equation of motion $\dot x=f(t)$, where $f(t)$ is a random function with statistics which are independent of $x$ and $t$, with a finite drift velocity $v=\langle f\rangle$ and in the presence of a…