64 citations · 883 across the 36 of their papers we have counts for
36 papers
Kawasaki dynamics beyond the uniqueness threshold
Roland Bauerschmidt, Thierry Bodineau, Benoit Dagallier
Glauber dynamics of the Ising model on a random regular graph is known to mix fast below the tree uniqueness threshold and exponentially slowly above it. We show that Kawasaki dyna…
Stochastic dynamics and the Polchinski equation: an introduction
Roland Bauerschmidt, Thierry Bodineau, Benoit Dagallier
This introduction surveys a renormalisation group perspective on log-Sobolev inequalities and related properties of stochastic dynamics. We also explain the relationship of this ap…
Log-Sobolev inequality for near critical Ising models
Roland Bauerschmidt, Benoit Dagallier
For general ferromagnetic Ising models whose coupling matrix has bounded spectral radius, we show that the log-Sobolev constant satisfies a simple bound expressed only in terms of…
Log-Sobolev inequality for the and measures
Roland Bauerschmidt, Benoit Dagallier
The continuum and measures are shown to satisfy a log-Sobolev inequality uniformly in the lattice regularisation under the optimal assumption that their susceptibil…
The Discrete Gaussian model, II. Infinite-volume scaling limit at high temperature
Roland Bauerschmidt, Jiwoon Park, Pierre-François Rodriguez
The Discrete Gaussian model is the lattice Gaussian free field conditioned to be integer-valued. In two dimensions, at sufficiently high temperature, we show that the scaling limit…
Spin systems with hyperbolic symmetry: a survey
Roland Bauerschmidt, Tyler Helmuth
Spin systems with hyperbolic symmetry originated as simplified models for the Anderson metal--insulator transition, and were subsequently found to exactly describe probabilistic mo…
Percolation transition for random forests in
Roland Bauerschmidt, Nicholas Crawford, Tyler Helmuth
The arboreal gas is the probability measure on (unrooted spanning) forests of a graph in which each forest is weighted by a factor per edge. It arises as the limit o…
The Coleman correspondence at the free fermion point
Roland Bauerschmidt, Christian Webb
We prove that the truncated correlation functions of the charge and gradient fields associated with the massless sine-Gordon model on with exist for all coupl…
Maximum and coupling of the sine-Gordon field
Roland Bauerschmidt, Michael Hofstetter
For , we prove that the distribution of the centred maximum of the -regularised continuum sine-Gordon field on the two-dimensional torus converges to a randomly shifted…
Random spanning forests and hyperbolic symmetry
Roland Bauerschmidt, Nicholas Crawford, Tyler Helmuth +1
We study (unrooted) random forests on a graph where the probability of a forest is multiplicatively weighted by a parameter per edge. This is called the arboreal gas model, a…
Mean-field tricritical polymers
Roland Bauerschmidt, Gordon Slade
We provide an introductory account of a tricritical phase diagram, in the setting of a mean-field random walk model of a polymer density transition, and clarify the nature of the d…
Edge rigidity and universality of random regular graphs of intermediate degree
Roland Bauerschmidt, Jiaoyang Huang, Antti Knowles +1
For random -regular graphs on vertices with , we develop a expansion of the local eigenvalue distribution about the Kesten-McKay law up to or…
Log-Sobolev inequality for the continuum sine-Gordon model
Roland Bauerschmidt, Thierry Bodineau
We derive a multiscale generalisation of the Bakry--Émery criterion for a measure to satisfy a Log-Sobolev inequality. Our criterion relies on the control of an associated PDE well…
Introduction to a renormalisation group method
Roland Bauerschmidt, David C. Brydges, Gordon Slade
This book provides an introduction to a renormalisation group method in the spirit of that of Wilson. It starts with a concise overview of the theory of critical phenomena and the…
Three-dimensional tricritical spins and polymers
Roland Bauerschmidt, Martin Lohmann, Gordon Slade
We consider two intimately related statistical mechanical problems on : (i) the tricritical behaviour of a model of classical unbounded -component continuous spins…
The geometry of random walk isomorphism theorems
Roland Bauerschmidt, Tyler Helmuth, Andrew Swan
The classical random walk isomorphism theorems relate the local times of a continuous-time random walk to the square of a Gaussian free field. A Gaussian free field is a spin syste…
Dislocation lines in three-dimensional solids at low temperature
Roland Bauerschmidt, Diana Conache, Markus Heydenreich +2
We propose a model for three-dimensional solids on a mesoscopic scale with a statistical mechanical description of dislocation lines in thermal equilibrium. The model has a lineari…
Spectral gap critical exponent for Glauber dynamics of hierarchical spin models
Roland Bauerschmidt, Thierry Bodineau
We develop a renormalisation group approach to deriving the asymptotics of the spectral gap of the generator of Glauber type dynamics of spin systems with strong correlations (at a…
Dynkin isomorphism and Mermin--Wagner theorems for hyperbolic sigma models and recurrence of the two-dimensional vertex-reinforced jump process
Roland Bauerschmidt, Tyler Helmuth, Andrew Swan
We prove the vertex-reinforced jump process (VRJP) is recurrent in two dimensions for any translation invariant finite range initial rates. Our proof has two main ingredients. The…
A very simple proof of the LSI for high temperature spin systems
Roland Bauerschmidt, Thierry Bodineau
We present a very simple proof that the model satisfies a uniform logarithmic Sobolev inequality (LSI) if the positive definite coupling matrix has largest eigenvalue less t…
Four-dimensional weakly self-avoiding walk with contact self-attraction
Roland Bauerschmidt, Gordon Slade, Benjamin C. Wallace
We consider the critical behaviour of the continuous-time weakly self-avoiding walk with contact self-attraction on , for sufficiently small attraction. We prove that…
Local Kesten--McKay law for random regular graphs
Roland Bauerschmidt, Jiaoyang Huang, Horng-Tzer Yau
We study the adjacency matrices of random -regular graphs with large but fixed degree . In the bulk of the spectrum down…
The two-dimensional Coulomb plasma: quasi-free approximation and central limit theorem
Roland Bauerschmidt, Paul Bourgade, Miika Nikula +1
For the two-dimensional one-component Coulomb plasma, we derive an asymptotic expansion of the free energy up to order , the number of particles of the gas, with an effective er…
Renormalisation group analysis of 4D spin models and self-avoiding walk
Roland Bauerschmidt, David C. Brydges, Gordon Slade
We give an overview of results on critical phenomena in 4 dimensions, obtained recently using a rigorous renormalisation group method. In particular, for the -component …