10 papers
Formation of clusters and coarsening in weakly interacting diffusions
Nicolai Gerber, Rishabh S. Gvalani, Martin Hairer +2
This paper studies the clustering behavior of weakly interacting diffusions under the influence of sufficiently localized attractive interaction potentials on the one-dimensional t…
How does the supercritical GMC converge?
Federico Bertacco, Martin Hairer
In the spirit of [M. Biskup & O. Louidor, Adv. Math. 330 (2018)], we study the local structure of -scale invariant fields -- a class of log-correlated Gaussian fields -- aro…
First Proof
Mohammed Abouzaid, Andrew J. Blumberg, Martin Hairer +8
To assess the ability of current AI systems to correctly answer research-level mathematics questions, we share a set of ten math questions which have arisen naturally in the resear…
Singularity of solutions to singular SPDEs
Martin Hairer, Seiichiro Kusuoka, Hirotatsu Nagoji
Building on the notes [Hai17], we give a sufficient condition for the marginal distribution of the solution of singular SPDEs on the -dimensional torus to be singular with respe…
Scaling Limits of a Weakly Perturbed Random Interface Model
PatrÃcia Gonçalves, Martin Hairer, Maria Chiara Ricciuti
We consider a random interface model on the discrete torus with sites, obtained from the classical corner flip dynamics but with a weak global perturbation, namely an asymmetr…
Uniqueness of supercritical Gaussian multiplicative chaos
Federico Bertacco, Martin Hairer
We show that, for general convolution approximations to a large class of log-correlated Gaussian fields, the properly normalised supercritical Gaussian multiplicative chaos measure…