64 citations · 883 across the 36 of their papers we have counts for
18 papers · 1 filter
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…
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…
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…
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…
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…
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…
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…
Bulk eigenvalue statistics for random regular graphs
Roland Bauerschmidt, Jiaoyang Huang, Antti Knowles +1
We consider the uniform random -regular graph on vertices, with for arbitrary . We prove that in the bulk of the spectrum the local eigenvalue…
Local semicircle law for random regular graphs
Roland Bauerschmidt, Antti Knowles, Horng-Tzer Yau
We consider random -regular graphs on vertices, with degree at least . We prove that the Green's function of the adjacency matrix and the Stieltjes transform…
Lectures on Self-Avoiding Walks
Roland Bauerschmidt, Hugo Duminil-Copin, Jesse Goodman +1
These lecture notes provide a rapid introduction to a number of rigorous results on self-avoiding walks, with emphasis on the critical behaviour. Following an introductory overview…
A simple method for finite range decomposition of quadratic forms and Gaussian fields
Roland Bauerschmidt
We present a simple method to decompose the Green forms corresponding to a large class of interesting symmetric Dirichlet forms into integrals over symmetric positive semi-definite…