Recent Developments on Mixing Times: March 17-21, 2025

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Organized by:

  • Evita Nestoridi ( Stony Brook University)
  • Dominik Schmid ( Bonn University)

Markov chains serve as indispensable tools for generating random structures, such as graph colorings, vector space bases, and polygon triangulations. Mixing times capture the temporal evolution towards equilibrium. Of particular interest is the abrupt transition from unmixed to mixed – the cutoff phenomenon. The cutoff phenomenon was first discovered by Diaconis and Shashahani in the context of card shuffling.  Many techniques from representation theory, combinatorics and probability, comparison theory, Nash inequalities, evolving sets, distinguishing statistics, and many more have been developed to understand mixing times. The question whether cutoff occurs was solved over the years for many models, for example random walks on random graphs, the card shuffles, or the east process. In recent years, many new techniques to verify the occurrence or absence of cutoff, as well as even more refined results on the convergence towards the stationary distribution, were established.

Our main goal is to bring together people with backgrounds from mathematical physics, probability theory and theoretical computer science, and develop new insights on mixing times. In particular, the interplay between the exciting new methods from recent years including information percolation, stochastic localization, and varentropy methods is promising towards improving the understanding of cutoff. Another goal is to strengthen the research on limit profiles, which are an exciting new objective in the study of mixing times for Markov chains.

 

Talk Schedule


Time Title Speaker Location
8:30am Breakfast N/A SCGP Cafe
9:30am TBA Jonathan Hermon SCGP 102
10:30am Coffee Break  N/A SCGP Cafe
11:00am Phase ordering for the Ising dynamics on random regular graphs Reza Gheissari N/A
12:00pm Lunch  N/A SCGP Cafe
1:30pm Ergodicity, mixing and classification of Gibbs states for area-tilted Brownian lines Shirshendu Ganguly SCGP 102
2:30pm 1) k-star transposition shuffle, 2) Mixing Time and Cutoff for the Capacity $k$, 3) Cutoff and Dynamical Phase Transition for the General Multi-componentIsing Model 1) Samira Arfaee, 2)  Eyob Tsegaye, 3) Seoyeon Yang SCGP 102
3:30pm Tea Time  N/A SCGP Cafe
4:00pm 1) Cutoff for a generalized Bernoulli-Laplace model, 2) Vector-Valued Concentration & Random Walks on Groups, 3) TBD 1) Ritesh Goenka, 2) Mira Gordin, 3) Yuhan Jiang SCGP 102

Time Title Speaker Location
8:30am Breakfast N/A SCGP Cafe
9:30am Cutoff phenomenon in nonlinear recombinations Cyril Labbe SCGP 102
10:30am Coffee Break  N/A SCGP Cafe
11:00am Mixing of energy redistribution models Matteo Quattropani SCGP 102
12:00pm Lunch  N/A SCGP Cafe
1:30pm Cutoff of the repeated average process on graphs Lingfu Zhang SCGP 102
2:30pm 1) Cutoff for the mixing time of the Facilitated Exclusion Process and the Symmetric, 2) Mixing of a random walk on a randomly twisted hypercube Exclusion Process with Traps, 3)Mixing of a random walk on a randomly twisted hypercube 1) Brune Massoulie, 2) Zsuzsanna Baran, 3) Andjela Sarkovic SCGP 102
3:30pm Tea Time  N/A SCGP Cafe
4:00pm 1) Cutoff for the Biased Random Transposition Shuffle, 2) A probabilistic parking process and labeled IDLA, 3) Accelerated Mixing in Markov chain Monte Carlo 1) Alan Yan, 2) Amanda Priestley, 3) Stefan Oberdorster N/A

Time Title Speaker Location
8:30am Breakfast N/A SCGP Cafe
9:30am Regularized functional inequalities, discrete curvature, and applications to Markov chains Pierre Youssef SCGP 102
10:30am Coffee Break  N/A SCGP Cafe
11:00am Cutoff for Cayley Graphs of Nilpotent Groups Xiangying (Zoe) Huang SCGP 102
12:00pm Lunch  N/A SCGP Cafe
12:00pm Group Photo N/A SCGP Lobby
1:30pm Curvature and concentration in time-inhomogeneous Markov chains, Luca Zanetti SCGP 102
2:30pm A Randomised Approach to Sorting Sam Olesker-Taylor N/A
3:30pm Tea Time  N/A SCGP Cafe
4:00pm Cutoff profiles for conjugacy invariant walks on symmetric groups Lucas Teyssier SCGP 102
4:40pm Limit profiles of ASEP Peter Nejjar SCGP 102
6:00pm Banquet Dinner  N/A SCGP Cafe

Time Title Speaker Location
8:30am Breakfast N/A SCGP Cafe
9:30am Sampling from the Potts model at low temperatures via random-cluster dynamics Antonio Blanca SCGP 102
10:30am Coffee Break  N/A SCGP Cafe
11:00am On sampling two spin models using the local connective constant Charis Efthymiou SCGP 102
12:00pm Lunch  N/A SCGP Cafe
1:30pm Simultaneous cutoff for Markov chains on the multitype configuration model Balazs Gerencser SCGP 102
2:30pm Spectral gap and cutoff of the simple exclusion process with IID conductances Shangjie Yang SCGP 102
2:30pm Mixing Time of the Glauber Dynamics for the Critical Ising Model on Sparse Graphs Kyprianos Iason-Prodomidis SCGP 102
3:30pm Tea Time  N/A SCGP Cafe
4:00pm Dynamics of Epidemics on Random Graphs Oanh Nguyen  SCGP 102
4:40pm Cutoff phenomenon for the ergodic CIR process and extensions Gerardo Barrera SCGP 102

Time Title Speaker Location
8:30am Breakfast N/A SCGP Cafe
9:30am Cutoff profile for the ASEP with one open boundary Jimmy He SCGP 102
10:30am Coffee Break  N/A SCGP Cafe
11:00am An information-differential approach to cutoff Justin Salez SCGP 102
12:00pm Lunch  N/A SCGP Cafe
3:30pm Tea Time  N/A SCGP Cafe