Ornstein-Zernike Theory for the 2D Near-critical Random Cluster Model

par Lucas D'Alimonte (Université de Fribourg)

vendredi 1 déc. 2023, 14:00 → 16:00 Europe/Paris

Amphithéâtre Léon Motchane (IHES)

Probability and analysis informal seminar

In this talk, we will discuss the classical Ornstein-Zernike theory for the random-cluster models (also known as FK percolation). In its modern form, it is a very robust theory, which most celebrated output is the computation of the asymptotically polynomial corrections to the pure exponential decay of the two-points correlation function of the random-cluster model in the subcritical regime. We will present an ongoing project that extends this theory to the near-critical regime of the two-dimensional random-cluster model, thus providing a precise understanding of the Ornstein-Zernike asymptotics when p approaches the critical parameter $p_c$. The output of this work is a formula encompassing both the critical behaviour of the system when looked at a scale negligible with respect to its correlation length, and its subcritical behaviour when looked at a scale way larger than its correlation length. Based on a joint work with Ioan Manolescu.

========

Pour être informé des prochains séminaires vous pouvez vous abonner à la liste de diffusion en écrivant un mail à sympa@listes.math.cnrs.fr avec comme sujet: "subscribe seminaire_mathematique PRENOM NOM"
(indiquez vos propres prénom et nom) et laissez le corps du message vide.