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Random walks on random simple graphs

✍ Scribed by Martin Hildebrand

Publisher: John Wiley and Sons
Year: 1996
Tongue: English
Weight: 676 KB
Volume: 8
Category: Article
ISSN: 1042-9832
DOI: 10.1002/(sici)1098-2418(199607)8:4<301::aid-rsa2>3.0.co;2-1

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✦ Synopsis

This paper looks at random regular simple graphs and considers nearest neighbor random walks on such graphs. This paper considers walks where the degree d of each vertex is around (logn)", where a is a constant which is at least 2 and where n is the number of vertices. By extending techniques of Dou, this paper shows that for most such graphs, the position of the random walk becomes close to uniformly distributed after slightly more than lognllogd steps. This paper also gets similar results for the random graph G(n, p).

where p = d/(n -1).

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