100, rue des maths 38610 Gières / GPS : 45.193055, 5.772076 / Directeur : Louis Funar

Lucas D'Alimonte

Ornstein--Zernike theory for the 2D near-critical random cluster model
Mardi, 2 Juillet, 2024 - 14:00 à 15:00
Résumé : 

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.

Institution de l'orateur : 
Université de Fribourg
Thème de recherche : 
Salle : 
salle 01 tour IRMA
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