This term, all seminars take place Thursdays at 2pm, room MS.05 (Zeeman Building), unless indicated otherwise.

Schedule for

Lenka Zdeborová, 31.01.2008



11.10.2018 Leonid Petrov (Virginia)
Nonequilibrium particle systems in inhomogeneous space
I will discuss stochastic interacting particle systems in the KPZ universality class evolving in one-dimensional inhomogeneous space. The inhomogeneity means that the speed of a particle depends on its location. I will focus on integrable examples of such systems, i.e., for which certain observables can be written in an exact form suitable for asymptotic analysis. Examples include a continuous-space version of TASEP (totally asymmetric simple exclusion process), and the pushTASEP (=long-range TASEP). For integrable systems, limiting density can be described in an explicit way. We obtain asymptotics of fluctuations, in particular, around slow bonds and infinite traffic lights.
Contact: Nikos
18.10.2018 Jonathan Hermon (University of Cambridge)
No percolation at criticality for groups with fast heat kernel decay
I will prove that there is no percolation at criticality on groups satisfying a heat kernel bound of the form p_n(v,v) < e^(-c n^gamma) for gamma > 1/2. This condition is known to hold for certain groups of intermediate growth. Joint work with Tom Hutchcroft.
Contact: Wei

01.11.2018 Khoa Le (Imperial College)
A stochastic sewing lemma and applications
We introduce a stochastic version of Gubinelli sewing lemma. While adaptiveness is required, the regularity restriction is improved by a half. To illustrate potential applications, we use the stochastic sewing lemma in studying stochastic differential equations driven by Brownian motions or fractional Brownian motions with irregular drifts.
Contact: Giuseppe

15.11.2018 David Dereudre (Lille)
Sharp phase transition for the continuum Widom-Rowlinson model
The Widom-Rowlinson model (or the Area-interaction model) is a Gibbs point process in Rd with the formal Hamiltonian define as the volume of unit balls centred at the points of the configuration. The model is tuned by two other parameters: the activity z > 0 related to the intensity of the process and the inverse temperature β ≥ 0 related to the strength of the interaction. We investigate the phase transition of the model in the point of view of percolation theory and the liquid-gas transition. First, considering the graph connecting points with distance smaller than 2r > 0, we show that for any β ≥ 0, there exists 0 < z(β, r) < +∞ such that an exponential decay of connectivity at distance n occurs in the subcritical phase (i.e. z < (β, r)) and a linear lower bound of the connection at infinity holds in the supercritical case (i.e. z > z(β, r)). These results are in the spirit of recent works using the theory of randomised tree algorithms. Secondly we study a standard liquid-gas phase transition related to the uniqueness/non-uniqueness of Gibbs states depending on the parameters z, β. Old results claim that a nonuniqueness regime occurs for z = β large enough and it is conjectured that the uniqueness should hold outside such an half line (z = β ≥ βc > 0). We solve partially this conjecture in any dimension by showing that for β large enough the non-uniqueness holds if and only if z = β. We show also that this critical value z = β corresponds to the percolation threshold z(β, r) = β for β large enough, providing a straight connection between these two notions of phase transition.
Contact: Stefan A
22.11.2018 Laurent Betermin (Copenhagen )
Lattice theta function and ionic crystal: a proof of Born’s conjecture

In his paper "Über elektrostatische Gitterpotentiale", published in 1921, Max Born asked the following question related to ionic crystals: "How to arrange positive and negative charges on a simple cubic lattice of finite extent so that the electrostatic energy is minimal?". He conjectured that the alternation of charges +1 and -1 is optimal distribution of charges. In this talk, I will explain a connection between the translated lattice theta function and the optimal configuration of charges on a given lattice, when the interaction potential is completely monotone. Thus, a proof of Born’s conjecture in any dimension, for orthorhombic lattices, will be given. Finally, we will see that the solution for the triangular lattice exhibits a surprising honeycomb structure. This talk is based on joint works with Hans Knüpfer (University of Heidelberg) and Mircea Petrache (PUC Chile).
Contact: Stefan A. & Florian
29.11.2018 Steffen Dereich (Münster)
Extended notions of local convergence for sequences of random graphs
Local convergence is also known as Benjamini-Schramm convergence is an analog of the Palm measure concept applicable to growing sequences of finite random graphs $(G_n)_{ninmathbb N}$. Here one centers the graph around a uniformly chosen vertex and considers distributional convergence (in an appropriate local sense) to a random rooted and connected graph $(G,o)$ (in most cases a tree). At least on an informal level, the local limit provides many insights about the structure of large graphs. For instance, the relative size of the largest component typically converges in probability to the probability that the graph $G$ is infinite. In this talk, we introduce newly extended notions of local convergence that incorporate additional information on the graph localised around a uniformly chosen vertex. In one variant we keep information on the shortest weight-path to a second uniformly chosen vertex which can be interpreted as the path along which an infection occurs. A second variant keeps track of the local visits of a random walk run on the random graph.
Contact: Stefan A
06.12.2018 Willem van Zuijlen (Weierstrass Institute)
Mass-asymptotics for the parabolic Anderson model in 2 d
I present work in progress with Wolfgang König and Nicolas Perkowski on the parabolic Anderson model (PAM) with white noise potential in 2d. We show the behavior of the total mass as the time tends to infinity, by using new stochastic characteristics and singular heat kernel estimates.
Contact: Giuseppe