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Partitions, a mock theta function, and probability

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Speaker: 
Karl Mahlburg
Affiliation: 
Princeton U.
Date: 
Wed, 2010-07-28 14:15 - 15:15
Location: 
MPIM Lecture Hall
Parent event: 
Number theory lunch seminar

I will discuss recent work with Kathrin Bringmann that begins with the study of an infinite family of hypergeometric q-series with alternating signs. These q-series first arose in combinatorial probability, in the problem of determining scaling exponents for bootstrap percolation models. However, they also have surprising connections to integer partitions without consecutive parts, and also to a finite Markov process for sequences with certain gap conditions; one of Ramanujan's famous mock theta functions also makes an appearance. One of our main results is a probabilistic proof of the cuspidal asymptotics of these hypergeometric series; there is no known number-theoretic proof for this result.

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