Mean-field Potts and random-cluster dynamics from high-entropy initializations
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 …
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
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 …
functional inequalities such as Poincar\'e inequalities. In many situations, Markov chains fail …
Sampling from the Potts model at low temperatures via Swendsen–Wang dynamics
A Blanca, R Gheissari - 2023 IEEE 64th Annual Symposium on …, 2023 - ieeexplore.ieee.org
Sampling from the q-state ferromagnetic Potts model is a fundamental question in statistical
physics, probability theory, and theoretical computer science. On general graphs, this …
physics, probability theory, and theoretical computer science. On general graphs, this …
Planting and MCMC Sampling from the Potts model
We consider the problem of sampling from the ferromagnetic $ q $-state Potts model on the
random $ d $-regular graph with parameter $\beta> 0$. A key difficulty that arises in …
random $ d $-regular graph with parameter $\beta> 0$. A key difficulty that arises in …
Sampling from the random cluster model on random regular graphs at all temperatures via Glauber dynamics
We consider the performance of Glauber dynamics for the random cluster model with real
parameter $ q> 1$ and temperature $\beta> 0$. Recent work by Helmuth, Jenssen and …
parameter $ q> 1$ and temperature $\beta> 0$. Recent work by Helmuth, Jenssen and …
On the tractability of sampling from the Potts model at low temperatures via random-cluster dynamics
A Blanca, R Gheissari - Probability Theory and Related Fields, 2024 - Springer
Sampling from the q-state ferromagnetic Potts model is a fundamental question in statistical
physics, probability theory, and theoretical computer science. On general graphs, this …
physics, probability theory, and theoretical computer science. On general graphs, this …
On the tractability of sampling from the Potts model at low temperatures via Swendsen--Wang dynamics
A Blanca, R Gheissari - arXiv preprint arXiv:2304.03182, 2023 - arxiv.org
Sampling from the $ q $-state ferromagnetic Potts model is a fundamental question in
statistical physics, probability theory, and theoretical computer science. On general graphs …
statistical physics, probability theory, and theoretical computer science. On general graphs …
Fast relaxation of the random field Ising dynamics
We study the convergence properties of Glauber dynamics for the random field Ising model
(RFIM) with ferromagnetic interactions on finite domains of $\mathbb {Z}^ d $, $ d\ge 2$. Of …
(RFIM) with ferromagnetic interactions on finite domains of $\mathbb {Z}^ d $, $ d\ge 2$. Of …
Geometry and Duality of Alternating Markov Chains
D Mithal, L Orecchia - arXiv preprint arXiv:2410.12721, 2024 - arxiv.org
We realize the half-steps of a general class of Markov chains as alternating projections with
respect to the reverse Kullback-Leibler divergence between sets of joint probability …
respect to the reverse Kullback-Leibler divergence between sets of joint probability …
Mixing phases of the Glauber dynamics for the -spin Curie-Weiss model
RJ Samanta, S Mukherjee, J Zhang - arXiv preprint arXiv:2412.16952, 2024 - arxiv.org
The Glauber dynamics for the classical $2 $-spin Curie-Weiss model on $ N $ nodes with
inverse temperature $\beta $ and zero external field is known to mix in time $\Theta (N\log …
inverse temperature $\beta $ and zero external field is known to mix in time $\Theta (N\log …