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Shuffling via transpositions

Introductory Workshop: Probability and Statistics of Discrete Structures January 27, 2025 - January 31, 2025

January 31, 2025 (03:30 PM PST - 04:30 PM PST)
Speaker(s): Evita Nestoridi (Stony Brook University)
Location: SLMath: Eisenbud Auditorium, Online/Virtual
Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC
Video

Shuffling via transpositions

Abstract

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In their seminal work, Diaconis and Shahshahani proved that shuffling a deck of $n$ cards sufficiently well via random transpositions takes $1/2 n log n$ steps. Their argument was algebraic and relied on the combinatorics of the symmetric group. In this talk, I will focus on two other shuffles, generalizing random transpositions and I will discuss the underlying combinatorics for understanding their mixing behavior and indeed proving cutoff. The talk will be based on joint works with A. Yan and S. Arfaee.

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Shuffling via transpositions

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