Related papers: Dirac walks on regular trees
Dirac fermions on a two-dimensional lattice with disorder are considered. The Dirac mass, which controls the gap between the two bands of the fermions, is subject to random fluctuations. Another type of disorder is discussed presented by a…
In this note, we compute the probability that a two-dimensional symmetric random walk visits more vertices than expected, for deviations on scales between the mean behavior and linear growth.
The purpose of these notes is to clarify the duality between a natural class of jump processes on compact ultrametric spaces - studied in current work of Bendikov, Girgor'yan and Pittet - and nearest neighbour walks on trees. Processes of…
Two-dimensional networks of ordered quantum dots beyond the percolation threshold are studied, as typical example of conducting nanostructures with quenched random disorder. Theory predicts anomalous diffusion with stretched-exponential…
Two-dimensional (random) walks in cones are very natural both in combinatorics and probability theory: they are interesting for themselves and also because they are strongly related to other discrete structures. While walks restricted to…
We study two-dimensional Dirac fermions in a random non-Abelian vector potential by using lattice regularization. We consider U(N) random vector potential for large $N$. The ensemble average with respect to random vector potential is taken…
We study a discrete random walk on a one-dimensional finite lattice, where each state has different probabilities to move one step forward, backward, staying for a moment or being absorbed. We obtain expected number of arrivals and expected…
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…
The problem of simulating through quantum walks Dirac fermions in arbitrary curved space-times and coordinates is revisited, taking (1 + 1)D space-times as an example. A new shift or translation operator on the grid is introduced, to take…
We analyze random walk through fractal environments, embedded in 3-dimensional, permeable space. Particles travel freely and are scattered off into random directions when they hit the fractal. The statistical distribution of the flight…
We introduce a continuous-time quantum walk on an ultrametric space corresponding to the set of p-adic integers and compute its time-averaged probability distribution. It is shown that localization occurs for any location of the ultrametric…
Motivated by the immense success of random walk and Markov chain methods in the design of classical algorithms, we consider_quantum_ walks on graphs. We analyse in detail the behaviour of unbiased quantum walk on the line, with the example…
Large unweighted directed graphs are commonly used to capture relations between entities. A fundamental problem in the analysis of such networks is to properly define the similarity or dissimilarity between any two vertices. Despite the…
A rotor configuration on a graph contains in every vertex an infinite ordered sequence of rotors, each is pointing to a neighbor of the vertex. After sampling a configuration according to some probability measure, a rotor walk is a…
A discrete-time Quantum Walk (QW) is essentially an operator driving the evolution of a single particle on the lattice, through local unitaries. Some QWs admit a continuum limit, leading to well-known physics partial differential equations,…
We use a one-dimensional random walk on $D$-dimensional hyper-spheres to determine the critical behavior of statistical systems in hyper-spherical geometries. First, we demonstrate the properties of such walk by studying the phase diagram…
Real networks are often dynamic. In response to it, analyses of algorithms on {\em dynamic networks} attract more and more attentions in network science and engineering. Random walks on dynamic graphs also have been investigated actively in…
It is a classic result in spectral theory that the limit distribution of the spectral measure of random graphs G(n, p) converges to the semicircle law in case np tends to infinity with n. The spectral measure for random graphs G(n, c/n)…
We study the random walk on dynamical percolation of $\mathbb{Z}^d$ (resp., the two-dimensional triangular lattice $\mathcal{T}$), where each edge (resp., each site) can be either open or closed, refreshing its status at rate $\mu\in…
We study quantum walks on general graphs from the point of view of scattering theory. For a general finite graph we choose two vertices and attach one half line to each. We are interested in walks that proceed from one half line, through…