Gady Kozma - The stirring process II.

Gady Kozma: The stirring process II. Aldous's spectral gap conjecture. The stirring process, or random walk walk on the symmetric group generated by transpositions, arises in multiple natural contexts: quantum mechanics, card shuffling and self-interacting random walks. It has been analyzed probabilistically and algebraically with success. We survey recent results, with some proofs.