Poisson--Dirichlet distribution for random Belyi surfaces

Details Poisson--Dirichlet distribution for random Belyi surfaces Poisson--Dirichlet distribution for random Belyi surfaces

2005-01-19

arxiv.org/abs/math/0501283v3

Annals of Probability 2006, Vol. 34, No. 5, 1827-1848

Mathematics

Probability

Published at http://dx.doi.org/10.1214/009117906000000223 in the Annals of Probability (http://www.imstat.org/aop/) by the Ins

Scientific paper

10.1214/009117906000000223

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 ``typical'' compact Riemann surface of large genus based on compactifying finite-area Riemann surfaces associated with random cubic graphs; by a theorem of Belyi, these are ``dense'' in the space of compact Riemann surfaces. The question as to how these surfaces are distributed in the Teichm\"{u}ller spaces depends on the study of oriented cycles in random cubic graphs with random orientation; Brooks and Makover conjectured that asymptotically normalized cycle lengths follow Poisson--Dirichlet distribution. We present a proof of this conjecture using representation theory of the symmetric group.

Affiliated with

Also associated with

No associations

Rating

Poisson--Dirichlet distribution for random Belyi surfaces does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Poisson--Dirichlet distribution for random Belyi surfaces, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Poisson--Dirichlet distribution for random Belyi surfaces will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-511594