Research Statement 1. Random Walks on Directed Graphs
نویسنده
چکیده
My research interests lie in spectral and extremal graph theory, as well as in the analysis of complex networks. A primary goal is to deduce fundamental structural graph properties from the spectrum of the graph or a few easily-computable invariants. In order to gain control over these invariants, extremal graph theory aims to tightly bound them and characterize the graphs achieving these bounds. Many of the problems I work on involve directed graphs and often require novel approaches, since many spectral tools only apply to the undirected case.
منابع مشابه
h . PR ] 1 5 Ja n 20 02 On the physical relevance of random walks : an example of random walks on a randomly oriented lattice ∗
Random walks on general graphs play an important role in the understanding of the general theory of stochastic processes. Beyond their fundamental interest in probability theory, they arise also as simple models of physical systems. A brief survey of the physical relevance of the notion of random walk on both undirected and directed graphs is given followed by the exposition of some recent resu...
متن کاملRandom Walks on Directed Covers of Graphs
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 equals the branching number, upper and lower growth rates do not longer coincide in general. Furthermore, the behaviour of random walks on directed covers of infi...
متن کاملNon-Backtracking Random Walks and a Weighted Ihara’s Theorem
We study the mixing rate of non-backtracking random walks on graphs by looking at non-backtracking walks as walks on the directed edges of a graph. A result known as Ihara’s Theorem relates the adjacency matrix of a graph to a matrix related to non-backtracking walks on the directed edges. We prove a weighted version of Ihara’s Theorem which relates the transition probability matrix of a non-ba...
متن کاملRandom walks on directed Cayley graphs
Previous authors have shown bounds on mixing time of random walks on finite undirected Cayley graphs, both with and without self-loops. We extend this to the most general case by showing that a similar bound holds for walks on all finite directed Cayley graphs. These are shown by use of two new canonical path theorems for mixing time of non-reversible Markov chains. The first result is related ...
متن کاملErratum: Transience and recurrence of rotor-router walks on directed covers of graphs
In the paper [4] Transience and recurrence of rotor-router walks on directed covers of graphs, published in ECP volume 17 (2012), no. 41 there is an error in the proof of Corollary 3.8. This corollary is essential for the transient part in the proof of Theorem 3.5(b). We fix this error by constructing a new rotor-router process, which fulfills our needs, and for which the statement of Corollary...
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تاریخ انتشار 2016