Related papers: Random-walk topological transition revealed via el…

Topological phase transitions can be described by the theory of critical phenomena and identified by critical exponents that define their universality classes. This is a consequence of the existence of a diverging length at the transition…

Topology describes properties of physical systems that remain constant under continuous deformations. For infinite vector waves, global topological invariants in position space are typically associated with periodic patterns. We demonstrate…

Quantum random walks are constructed on operator spaces with the aid of matrix-space lifting, a type of ampliation intermediate between those provided by spatial and ultraweak tensor products. Using a form of Wiener-Ito decomposition, a…

It is well known that many real world networks have the power-law degree distribution (scale-free property). However there are no rigorous results for continuous-time quantum walks on such realistic graphs. In this paper, we analyze…

A random walk is a basic stochastic process on graphs and a key primitive in the design of distributed algorithms. One of the most important features of random walks is that, under mild conditions, they converge to a stationary distribution…

We consider a system consisting of a planar random walk on a square lattice, submitted to stochastic elementary local deformations. Depending on the deformation transition rates, and specifically on a parameter $\eta$ which breaks the…

Random walks are basic diffusion processes on networks and have applications in, for example, searching, navigation, ranking, and community detection. Recent recognition of the importance of temporal aspects on networks spurred studies of…

Stochastic systems feature, in general, both coherent dynamics and incoherent transitions between different states. We propose a method to identify the coherent part in the full counting statistics for the transitions. The proposal is…

We investigate the genuinely quantum features of continuous-time quantum walks by combining a single-time and a multi-time quantifier of nonclassicality. On the one hand, we consider the quantum-classical dynamical distance…

This survey is concerned with random walks on mapping class groups. We illustrate how the actions of mapping class groups on Teichm\"uller spaces or curve complexes reveal the nature of random walks, and vice versa. Our emphasis is on the…

In this article we address the problem of the nonlinear interaction of subdiffusive particles. We introduce the random walk model in which statistical characteristics of a random walker such as escape rate and jump distribution depend on…

The behaviour of random quantum walks is known to be diffusive. Here we study discrete time quantum walks in weak stochastic gauge fields. In the case of position and spin dependent gauge field, we observe a transition from ballistic to…

We study a random walk in random environment on the non-negative integers. The random environment is not homogeneous in law, but is a mixture of two kinds of site, one in asymptotically vanishing proportion. The two kinds of site are (i)…

The direct measurement of topological invariants in both engineered and naturally occurring quantum materials is a key step in classifying quantum phases of matter. Here we motivate a toolbox based on time-dependent quantum walks as a…

Random walk models, such as the trap model, continuous time random walks, and comb models exhibit weak ergodicity breaking, when the average waiting time is infinite. The open question is: what statistical mechanical theory replaces the…

In this article, the continuous time random walk on the circle is studied. We derive the corresponding generalized master equation and discuss the effects of topology, especially important when Levy flights are allowed. Then, we work out…

We consider a one-dimensional continuous time random walk with transition rates depending on an underlying autonomous simple symmetric exclusion process starting out of equilibrium. This model represents an example of a random walk in a…

Although quantum walks exhibit peculiar properties that distinguish them from random walks, classical behavior can be recovered in the asymptotic limit by destroying the coherence of the pure state associated to the quantum system. Here I…

The relation between thermodynamic phase transitions in classical systems and topology changes in their state space is discussed for systems in which equivalence of statistical ensembles does not hold. As an example, the spherical model…

In this paper we introduce the notion of Random Walk in Changing Environment - a random walk in which each step is performed in a different graph on the same set of vertices, or more generally, a weighted random walk on the same vertex and…