Events calendar

We will discuss some aspects of two dynamics, motivated from cosmology but which originally appeared

in hydrodynamics, statistical physics and condensed matter, the Burgers and the Gross-Pitaevskii equations.

In the first part, we will present a simple solvable case in 1D with Poisson initial conditions.

In the second part, we will discuss the formation of dark matter vortices (as in superfluids).

Nous étudions la percolation FK où les paramètres des arêtes sont choisis comme des variables aléatoires indépendantes dans le régime proche-critique. Nous montrons que si ces paramètres satisfont une condition naturelle de centrage autour du point critique, alors le modèle quenched présente typiquement un comportement critique à des échelles bien plus grandes que la longueur caractéristique déterministe. Plus précisément, dans une boîte de taille N, si le modèle homogène avec un paramètre d’arête déterministe p a un comportement critique dans le régime |p − pc| ≤ W, alors le modèle quenched avec des paramètres d’arête aléatoires p qui satisfont typiquement |p − pc| ≤ W^{1/3} a encore un comportement critique. Nous traitons également le cas particulier de la percolation de Bernoulli, où nous montrons que si l’on commence par échantillonner des paramètres d’arêtes aléatoires indépendants non dégénérés centrés autour de 1/2, puis une configuration de percolation sur ces arêtes, le modèle quenched  est presque sûrement critique à grande échelle. Basé sur un travail avec Emile Avérous, disponible sur arXiv 2509.08938.

We use stellar dynamics as a testbed for statistical closure theory. We focus on the process of “Vector Resonant Relaxation,” a long-range, non-linear, and correlated relaxation mechanism that drives the reorientation of stellar orbital planes around a supermassive black hole. This process provides a natural setting to evaluate the predictive power of generic statistical closure schemes for dynamical correlation functions, in the fully non-linear and non-perturbative regime. We develop a numerical scheme that explicitly implements the seminal “Martin-Siggia-Rose” formalism at one-loop order via an iterative fixed-point approach, thereby improving upon the bare order from the “Direct Interaction Approximation.” Using this framework, we quantitatively validate the ability of the formalism to predict (i) the two-point two-time correlation function; (ii) the renormalised three-point interaction vertex; (iii) the three-point three-time correlation function. These predictions are compared to direct measurements from numerical simulations. We conclude by discussing the limitations of this approach and presenting possible future venues.

TBA

Abstract: 

(i) We study the statistics of stretched two-dimensional random walks (Brownian bridges) in the vicinity of an impermeable disc using the optimal–fluctuation approach. We show that the transverse span of the walks away from the boundary scales with the Kardar–Parisi–Zhang (KPZ) exponent $1/3$. (ii) Using the analogy between the optimal fluctuation in this setting and that in the one-dimensional Balagurov–Vaks trapping problem, we propose a connection between KPZ-like statistics and Lifshitz tails arising in a deterministic large-deviation landscape. (iii) By interpreting the radial component of the random walk above the disc as diffusion in a conformally invariant $1/r^{2}$ potential, we recover the Efimov–BKT behavior of the associated renormalization-group flow. From a large-deviation perspective, we argue that the typical paths responsible for the BKT-like behavior belong to a sub-ensemble of stretched Brownian bridges driven into the large-deviation regime.

TBA