Related papers: Efficient approximate unitary designs from random …
Rotor walk is a deterministic analogue of simple random walk. For any given graph, we construct a rotor configuration for which the escape rate of the corresponding rotor walk is equal to the escape rate of simple random walk, and thus…
We make and generalize the observation that summing of probability amplitudes of a discrete-time quantum walk over partitions of the walking graph consistent with the step operator results in a unitary evolution on the reduced graph which…
We prove new mixing rate estimates for the random walks on homogeneous spaces determined by a probability distribution on a finite group $G$. We introduce the switched random walk determined by a finite set of probability distributions on…
In this paper we consider the one-dimensional quantum random walk X^{varphi} _n at time n starting from initial qubit state varphi determined by 2 times 2 unitary matrix U. We give a combinatorial expression for the characteristic function…
Quantum walks on graphs can model physical processes and serve as efficient tools in quantum information theory. Once we admit random variations in the connectivity of the underlying graph, we arrive at the problem of percolation, where the…
We consider a transitive action of a finitely generated group $G$ and the Schreier graph $\Gamma$ defined by this action for some fixed generating set. For a probability measure $\mu$ on $G$ with a finite first moment we show that if the…
We evaluate the probabilities of various events under the uniform distribution on the set of 312-avoiding permutations of 1,...,N. We derive exact formulas for the probability that the ith element of a random permutation is a specific value…
We consider random walks in which the walk originates in one set of nodes and then continues until it reaches one or more nodes in a target set. The time required for the walk to reach the target set is of interest in understanding the…
We consider a random walk on the mapping class group of a surface of finite type. We assume that the random walk is determined by a probability measure whose support is finite and generates a non-elementary subgroup $H$. We further assume…
We consider two random walks evolving synchronously on a random out-regular graph of $n$ vertices with bounded out-degree $r\ge 2$, also known as a random Deterministic Finite Automaton (DFA). We show that, with high probability with…
The rate of convergence of simple random walk on the Heisenberg group over $Z/nZ$ with a standard generating set was determined by Bump et al [1,2]. We extend this result to random walks on the same groups with an arbitrary minimal…
Incorporating higher-order interactions in information processing enables us to build more accurate models, gain deeper insights into complex systems, and address real-world challenges more effectively. However, existing methods, such as…
A measure on a locally compact group is called spread out if one of its convolution powers is not singular with respect to Haar measure. Using Markov chain theory, we conduct a detailed analysis of random walks on homogeneous spaces with…
We derive "quenched" subdiffusive lower bounds for the exit time tau(n) from a box of size n for the simple random walk on the planar invasion percolation cluster. The first part of the paper is devoted to proving an almost sure analog of…
We study the isoperimetric and spectral profiles of certain families of finitely generated groups defined via actions on labelled Schreier graphs and simple {\em gluing} of such. In one of our simplest constructions---the {\em…
Random walk is an explainable approach for modeling natural processes at the molecular level. The Random Permutation Set Theory (RPST) serves as a framework for uncertainty reasoning, extending the applicability of Dempster-Shafer Theory.…
This paper considers a classical question of approximation of Brownian motion by a random walk in the setting of a sub-Riemannian manifold $M$. To construct such a random walk we first address several issues related to the degeneracy of…
In the frequency domain, the nearly constant loss, is characterized by a slope 1 in log of the real part of the electrical conductivity vs log frequency plots. It can be explained by an anomalous diffusion, defined by a random walk with the…
We consider the problem of performing a random walk in a distributed network. Given bandwidth constraints, the goal of the problem is to minimize the number of rounds required to obtain a random walk sample. Das Sarma et al. [PODC'10] show…
In this paper, we introduce a quantum walk whose local scattering at each vertex is denoted by a unitary circulant matrix; namely the circulant quantum walk. We also introduce another quantum walk induced by the circulant quantum walk;…