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Megan Bernstein, Georgia TechMegan Bernstein, Georgia TechEWG 336Title: Cutoff for the random to random shuffle Abstract: (joint work with Evita Nestoridi) The random to random shuffle on a deck of cards is given by at each step choosing a random card from the deck, removing it, and replacing it in a random location. We show an upper bound for the mixing time of the walk of 3/4n log(n) +cn steps. Together with matching lower bound of Subag (2013), this shows the walk mixes with cutoff at 3/4n log(n) steps, answering a conjecture of Diaconis. We use the diagonalization of the walk by Dieker and Saliola (2015), which relates the eigenvalues to Young tableaux. 3/20/2017 5:30:00 PM3/20/2017 6:30:00 PMFalse
Harry Crane, Rutgers UniversityHarry Crane, Rutgers UniversityEWG 336Title: Some aspects of random combinatorial structures Abstract: I will present some topics on the general theme of combinatorial stochastic processes. The discussion will be framed around observations that emerge from the study of Markov processes on arbitrary combinatorial spaces, of which partition- and graph-valued processes are special cases. I draw some connections to prior work on coalescent processes and graph limits and also highlight some potential open questions in this area. 3/13/2017 5:30:00 PM3/13/2017 6:30:00 PMFalse
Andrey Sarantsev, University of CaliforniaAndrey Sarantsev, University of CaliforniaEWG 336Title: Competing Brownian Particles Abstract: We study finite and infinite systems of Brownian particles on the real line with drift and diffusion coefficients depending on the current rank relative to other particles. We survey results obtained in the last decade and present some unsolved questions. 3/6/2017 6:30:00 PM3/6/2017 7:30:00 PMFalse
Ting Wang, University of DelawareTing Wang, University of DelawareEwg 336Title: Accelerated Stationary Distribution Sampling for Multiscale Stochastic Reaction Networks Abstract: Sampling of the steady state distribution of a multiscale stochastic dynamical system is challenging due to the time scale disparity in the underlying dynamics. Based on the parallel replica method, we propose an efficient algorithm for simulating multiscale continuous time Markov chains. Unlike most accelerated algorithms in computational chemistry, the algorithm we proposed does not rely on the detailed balance assumption. Furthermore, the algorithm can be easily combined with the path-space information bounds for sensitivity estimation. We apply the proposed algorithm to estimate the stationary averaging for stochastic chemical kinetics. Results from joint work with D. Aristoff on error analysis will be presented.2/20/2017 6:30:00 PM2/20/2017 7:30:00 PMFalse

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