Metastability of the Potts ferromagnet on random regular graphs

A Coja-Oghlan, A Galanis, LA Goldberg… - … in Mathematical Physics, 2023 - Springer
We study the performance of Markov chains for the q-state ferromagnetic Potts model on
random regular graphs. While the cases of the grid and the complete graph are by now well …

Mean-field Potts and random-cluster dynamics from high-entropy initializations

A Blanca, R Gheissari, X Zhang - Proceedings of the 2025 Annual ACM-SIAM …, 2025 - SIAM
A common obstruction to efficient sampling from high-dimensional distributions with Markov
chains is the multimodality of the target distribution because they may get trapped far from …

Weak Poincar\'e Inequalities, Simulated Annealing, and Sampling from Spherical Spin Glasses

B Huang, S Mohanty, A Rajaraman, DX Wu - arxiv preprint arxiv …, 2024 - arxiv.org
There has been a recent surge of powerful tools to show rapid mixing of Markov chains, via
functional inequalities such as Poincar\'e inequalities. In many situations, Markov chains fail …

Cutoff for nonbacktracking random walks on sparse random graphs

A Ben-Hamou, J Salez - 2017 - projecteuclid.org
A finite ergodic Markov chain exhibits cutoff if its distance to stationarity remains close to 1
over a certain number of iterations and then abruptly drops to near 0 on a much shorter time …

Swendsen‐Wang algorithm on the mean‐field Potts model

A Galanis, D Štefankovič… - Random Structures & …, 2019 - Wiley Online Library
We study the q‐state ferromagnetic Potts model on the n‐vertex complete graph known as
the mean‐field (Curie‐Weiss) model. We analyze the Swendsen‐Wang algorithm which is a …

[HTML][HTML] Tunneling behavior of Ising and Potts models in the low-temperature regime

FR Nardi, A Zocca - Stochastic Processes and their Applications, 2019 - Elsevier
We consider the ferromagnetic q-state Potts model with zero external field in a finite volume
and assume that its stochastic evolution is described by a Glauber-type dynamics …

Efficiently learning and sampling multimodal distributions with data-based initialization

F Koehler, H Lee, TD Vuong - arxiv preprint arxiv:2411.09117, 2024 - arxiv.org
We consider the problem of sampling a multimodal distribution with a Markov chain given a
small number of samples from the stationary measure. Although mixing can be arbitrarily …

Mixing times of critical two‐dimensional Potts models

R Gheissari, E Lubetzky - Communications on Pure and …, 2018 - Wiley Online Library
We study dynamical aspects of the q‐state Potts model on an n× n box at its critical βc (q).
Heat‐bath Glauber dynamics and cluster dynamics such as Swendsen–Wang (that …

Dynamics for the mean-field random-cluster model

A Blanca, A Sinclair - arxiv preprint arxiv:1412.6180, 2014 - arxiv.org
The random-cluster model is a unifying framework for studying random graphs, spin systems
in physics and random spanning trees. The model is closely related to, though much more …

Random-cluster dynamics on random regular graphs in tree uniqueness

A Blanca, R Gheissari - Communications in Mathematical Physics, 2021 - Springer
We establish rapid mixing of the random-cluster Glauber dynamics on random\varDelta Δ-
regular graphs for all q ≥ 1 q≥ 1 and p< p_u (q,\varDelta) p< pu (q, Δ), where the threshold …