Random oriented paths constrained by area trap

16.05.2022 15:15 – 17:15

We study a model of random oriented paths in the first quadrant of $\Z^2$ that demonstrates ubiquitous characteristics of the so-called KPZ universality class: scaling exponents of $2/3$ for the spatial correlations, $1/3$ for the fluctuations, local Brownian fluctuations and globally parabolic interfaces. We overcome the lack of integrability of the model using one essential tool: a method of "resampling" which consists in randomly replacing a portion of a path so that the law of the output remains the same. These techniques, which can be interpreted as a form of spatial Markov property or Gibbs property of the model, were developed by Alan Hammond in the study of subcritical clusters of FK percolation on $\Z^2$.

Lieu

Salle 1-15, Séminaire "Mathématique physique"

Organisé par

Faculté des sciences
Section de mathématiques

Intervenant-e-s

Romain Panis, University of Geneva
Lucas D'Alimonte, University of Fribourg

entrée libre

Classement

Catégorie: Séminaire

Mots clés: KPZ universality class, Brownian fluctuations, Alan Hammond