Related papers: Random Walks and Evolving Sets: Faster Convergence…
Under the assumption that sequences of graphs equipped with resistances, associated measures, walks and local times converge in a suitable Gromov-Hausdorff topology, we establish asymptotic bounds on the distribution of the…
We introduce a cover time problem for random walks on dynamic graphs in which the graph expands in time and the walker moves at random times. Time to cover all nodes and number of returns to original states are analyzed in resulting model.
An algorithm observes the trajectories of random walks over an unknown graph $G$, starting from the same vertex $x$, as well as the degrees along the trajectories. For all finite connected graphs, one can estimate the number of edges $m$ up…
The mixing time of a random walk, with or without backtracking, on a random graph generated according to the configuration model on $n$ vertices, is known to be of order $\log n$. In this paper we investigate what happens when the random…
In [1], the authors consider a random walk $(Z_{n,1},\ldots,Z_{n,K+1})\in \mathbb{Z}^{K+1}$ with the constraint that each coordinate of the walk is at distance one from the following one. A functional central limit theorem for the first…
We study the asymptotics of the $p$-mapping model of random mappings on $[n]$ as $n$ gets large, under a large class of asymptotic regimes for the underlying distribution $p$. We encode these random mappings in random walks which are shown…
Graph sampling is a technique to pick a subset of vertices and/ or edges from original graph. Among various graph sampling approaches, Traversal Based Sampling (TBS) are widely used due to low cost and feasibility for many cases, in which…
Directed covers of finite graphs are also known as periodic trees or trees with finitely many cone types. We expand the existing theory of directed covers of finite graphs to those of infinite graphs. While the lower growth rate still…
We obtain bivariate asymptotics for the number of (unicellular) combinatorial maps (a model of discrete surfaces) as both the size and the genus grow. This work is related to two research topics that have been very active recently:…
Focusing on coupling between edges, we generalize the relationship between the normalized graph Laplacian and random walks on graphs by devising an appropriate normalization for the Hodge Laplacian -- the generalization of the graph…
This paper investigates the Einstein relation; the connection between the volume growth, the resistance growth and the expected time a random walk needs to leave a ball on a weighted graph. The Einstein relation is proved under different…
Random walks are studied on disordered cellular networks in 2-and 3-dimensional spaces with arbitrary curvature. The coefficients of the evolution equation are calculated in term of the structural properties of the cellular system. The…
This paper considers non-backtracking random walks on random graphs generated according to the configuration model. The quantity of interest is the scaling of the mixing time of the random walk as the number of vertices of the random graph…
A survey is presented of known results concerning simple random walk on the class of distance-regular graphs. One of the highlights is that electric resistance and hitting times between points can be explicitly calculated and given strong…
The problem of a restricted random walk on graphs which keeps track of the number of immediate reversal steps is considered by using a transfer matrix formulation. A closed-form expression is obtained for the generating function of the…
Motivated by novel results in the theory of complex adaptive systems, we analyze the dynamics of random walks in which the jumping probabilities are {\it time-dependent}. We determine the survival probability in the presence of an absorbing…
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…
The main purpose of this thesis is to study the interplay between geometric properties of infinite graphs and analytic and probabilistic objects such as transition operators, harmonic functions and random walks on these graphs. For a…
We extend the use of random evolving sets to time-varying conductance models and utilize it to provide tight heat kernel upper bounds. It yields the transience of any uniformly lazy random walk, on Z^d, d>=3, equipped with uniformly bounded…
In this paper we address the problem of understanding the success of algorithms that organize patches according to graph-based metrics. Algorithms that analyze patches extracted from images or time series have led to state-of-the art…