10 papers
Spectral expansion of LQG heat trace and KPZ scaling
Nathanaël Berestycki, Jakob Klein
Let be a whole plane Gaussian free field, and let be a bounded domain in two dimensions. We study the asymptotics as of the Liouville quantum gravity (LQG) heat t…
The self-dual point of Fortuin--Kasteleyn planar maps is critical
Nathanaël Berestycki, William Da Silva
We study the Fortuin--Kasteleyn model of planar maps with parameter at and away from its self-dual point. This model is also bijectively equivalent to the fully packed…
Massive holomorphicity of near-critical dimers and sine-Gordon model
Nathanaël Berestycki, Scott Mason, Lucas Rey
In this paper, we consider the near-critical dimer model in the setup of isoradial superpositions with Temperleyan boundary conditions. We show that the centered height function co…
Brownian paths as loop-decorated SLEs
Nathanaël Berestycki, Isao Sauzedde
We construct an application, which takes as input a simple path and a possibly infinite collection of loops, and outputs a continuous path by adding the loops chronologically to th…
On the universality of fluctuations for the cover time
Nathanaël Berestycki, Jonathan Hermon, Lucas Teyssier
We consider random walks on finite vertex-transitive graphs of bounded degree. We find a simple geometric condition which characterises the cover time fluctuations: the suitab…
Stationary hitting times on vertex-transitive graphs
Nathanaël Berestycki, Jonathan Hermon, Lucas Teyssier
We prove a refined version of the Aldous and Brown's exponential approximation of stationary hitting times. These are valid for all reversible Markov chains. We then specialise our…