Student Probability Seminar

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Some Problems of Random Cycles - and How to Fix Them

Speaker: Guillaume Dubach

Location: Warren Weaver Hall 905

Date: Monday, March 6, 2017, 11 a.m.

Synopsis:

We shall consider the uniform distribution over the permutation groups and try to answer simple questions such as : how likely is it for two elements to belong to the same cycle ? How are fixed points distributed ? What is the typical size of a cycle ?... Some of our answers will be just as simple as the questions; whereas others will require to introduce usual tools and methods of random permutation theory, such as the celebrated Feller coupling, thanks to which we might even end up answering questions we didn't ask.