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math.PR2007★ 31 cited
On the girth of random Cayley graphs
Alex Gamburd, Shlomo Hoory, Mehrdad Shahshahani +2
We prove that random d-regular Cayley graphs of the symmetric group asymptotically almost surely have girth at least (log_{d-1}|G|)^{1/2}/2 and that random d-regular Cayley graphs…
math.PR2005★ 32 cited
Poisson--Dirichlet distribution for random Belyi surfaces
Alex Gamburd
Brooks and Makover introduced an approach to studying the global geometric quantities (in particular, the first eigenvalue of the Laplacian, injectivity radius and diameter) of a `…