Related papers: Heat kernel estimates for strongly recurrent rando…
We study the random graph obtained by random deletion of vertices or edges from a random graph with given vertex degrees. A simple trick of exploding vertices instead of deleting them, enables us to derive results from known results for…
We consider random walk on the structure given by a random hypergraph in the regime where there is a unique giant component. We give the asymptotics for hitting times, cover times, and commute times and show that the results obtained for…
We consider integer-valued random walks with independent but not identically distributed increments, and extend to this context several classical estimates, including a local limit theorem, precise small-ball estimates (both conditional on…
It is shown how to construct quantum random walks with particles in an arbitrary faithful normal state. A convergence theorem is obtained for such walks, which demonstrates a thermalisation effect: the limit cocycle obeys a quantum…
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…
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…
It is known that a random walk on $\Z^d$ among i.i.d. uniformly elliptic random bond conductances verifies a central limit theorem. It is also known that approximations of the covariance matrix can be obtained by considering periodic…
We propose a novel approach to parameter estimation for simulator-based statistical models with intractable likelihood. Our proposed method involves recursive application of kernel ABC and kernel herding to the same observed data. We…
We bound the rate of convergence to uniformity for certain random walks on the complete monomial groups G \wr S_n for any group G. These results provide rates of convergence for random walks on a number of groups of interest: the…
Random graphs have played an instrumental role in modelling real-world networks arising from the internet topology, social networks, or even protein-interaction networks within cells. Percolation, on the other hand, has been the fundamental…
We obtain expected number of arrivals, absorption probabilities and expected time until absorption for an asymmetric discrete random walk on a graph in the presence of multiple function barriers. On each edge of the graph and in each vertex…
We consider simple random walk on a realization of an Erd\H{o}s-R\'enyi graph that is asymptotically almost surely (a.a.s.) connected. We show a Central Limit Theorem (CLT) for the average starting hitting time, i.e. the expected time it…
We obtain matching two sided estimates of the heat kernel on a connected sum of parabolic manifolds, each of them satisfying the Li-Yau estimate. The key result is the on-diagonal upper bound of the heat kernel at a central point. Contrary…
We show how to compute the probabilities of various connection topologies for uniformly random spanning trees on graphs embedded in surfaces. As an application, we show how to compute the "intensity" of the loop-erased random walk in…
We study the heat content on quantum graphs and investigate whether an analogon of the Rayleigh-Faber-Krahn inequality holds. This means that heat content at time $T$ among graphs of equal volume would be maximized by intervals (the graph…
We study the behavior of the random walk on the infinite cluster of independent long range percolation in dimensions $d=1,2$, where $x$ and $y$ a re connected with probability $\sim\beta/\|x-y\|^{-s}$. We show that when $d<s<2d$ the walk is…
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…
We consider random walks on random graphs, focusing on return probabilities and hitting times for sparse Erdos-Renyi graphs. Using the tree approach which is expected to be exact in the large graph limit, we show how to solve for the…
This paper is concerned about random walks on random environments in the lattice $\mathbb{Z}^d$. This model is analyzed through ergodicity in the form of the logarithmic Sobolev inequality. We assume that the environments are random…
We investigate the hitting times of random walks on graphs, where a hitting time is defined as the number of steps required for a random walker to move from one node to another. While much of the existing literature focuses on calculating…