Alistair Sinclair

About

Alistair Sinclair is a professor in the Department of Statistics at the University of California, Berkeley. His research interests include algorithms, applied probability, random walks, Markov chains, computational applications of randomness, Markov chain Monte Carlo, statistical physics, and combinatorial optimization. Most of his work involves applying probabilistic ideas to design or analyze algorithms, with a focus on theoretical computer science, randomized computation, phase transitions, and nonlinear dynamical systems.

Research topics

• Mathematics
• Combinatorics
• Discrete mathematics
• Computer science
• Statistical physics

Selected publications

• Low-temperature Ising dynamics with random initializations

  2022-06-09 · 13 citations

  preprintOpen accessSenior author

  Glauber dynamics on spin systems are well known to suffer exponential slowdowns at low temperatures due to the emergence of multiple metastable phases, separated by narrow bottlenecks that are hard for the dynamics to cross. It is a folklore belief that if the dynamics is initialized from an appropriate random mixture of ground states, one for each phase, then convergence to the Gibbs distribution should be much faster. However, such phenomena have largely evaded rigorous analysis, as most tools…

  PublisherOA PDFDOI

• Correlation Decay and Partition Function Zeros: Algorithms and Phase Transitions

  SIAM Journal on Computing · 2022-07-26 · 12 citations

  articleOpen access

  We explore connections between the phenomenon of correlation decay (more precisely, strong spatial mixing) and the location of Lee--Yang and Fisher zeros for various spin systems. In particular we show that, in many instances, proofs showing that weak spatial mixing on the Bethe lattice (infinite $\Delta$-regular tree) implies that strong spatial mixing on all graphs of maximum degree $\Delta$ can be lifted to the complex plane, establishing the absence of zeros of the associated partition funct…

  PublisherOA PDFDOI

• Entropy decay in the Swendsen–Wang dynamics on ℤ ^<i>d</i>

  2021-06-15 · 12 citations

  article

  We study the mixing time of the Swendsen-Wang dynamics for the ferromagnetic Ising and Potts models on the integer lattice ℤd. This dynamics is a widely used Markov chain that has largely resisted sharp analysis because it is non-local, i.e., it changes the entire configuration in one step. We prove that, whenever strong spatial mixing (SSM) holds, the mixing time on any n-vertex cube in ℤd is O(logn), and we prove this is tight by establishing a matching lower bound. The previous best known bou…

  PublisherDOI

• The critical mean-field Chayes–Machta dynamics

  Combinatorics Probability Computing · 2022-05-11 · 5 citations

  articleOpen access

  Abstract The random-cluster model is a unifying framework for studying random graphs, spin systems and electrical networks that plays a fundamental role in designing efficient Markov Chain Monte Carlo (MCMC) sampling algorithms for the classical ferromagnetic Ising and Potts models. In this paper, we study a natural non-local Markov chain known as the Chayes–Machta (CM) dynamics for the mean-field case of the random-cluster model, where the underlying graph is the complete graph on n vertices. T…

  PublisherOA PDFDOI

• Spatial mixing and the random-cluster dynamics on lattices

  Society for Industrial and Applied Mathematics eBooks · 2023-01-01 · 4 citations

  book-chapterSenior author

  An important paradigm in the understanding of mixing times of Glauber dynamics for spin systems is the correspondence between spatial mixing properties of the models and bounds on the mixing time of the dynamics. This includes, in particular, the classical notions of weak and strong spatial mixing, which have been used to show the best known mixing time bounds in the high-temperature regime for the Glauber dynamics for the Ising and Potts models. Glauber dynamics for the random-cluster model doe…

  PublisherDOI

Recent grants

• AF: Small: Random Processes, Statistical Physics and Computation

  NSF · $450k · 2014–2018

• AF: Small: Approximate Counting, Stochastic Local Search and Nonlinear Dynamics

  NSF · $500k · 2018–2023

• AF: Medium: Collaborative Research: Information Compression in Algorithm Design and Statistical Physics

  NSF · $286k · 2015–2019

Frequent coauthors

• Piyush Srivastava

  Tata Institute of Fundamental Research

  48 shared

• Claire Kenyon

  33 shared

• Dorit S. Hochbaum

  University of California, Berkeley

  27 shared

• Bruno Petazzoni

  Laboratoire de l'Informatique du Parallélisme

  25 shared

• Maxime Crochemore

  Centre National de la Recherche Scientifique

  25 shared

• Mike Grigoriadis

  Laboratoire de l'Informatique du Parallélisme

  25 shared

• Uriel Feige

  25 shared

• Nicolas Puech

  Télécom Paris

  25 shared

Similar researchers at University of California, Berkeley

• Michael I. Jordanh-175
• Jennifer Chayesh-74
• Matei Zahariah-64