Workshop YEP XVII: "Interacting Particle Systems"
Aug 30 - Sep 3
Format
The workshop will take place in the week Aug 30 - Sep 3, 2021.
The event will be online.
Summary
The theory of Interacting Particle Systems focuses on the dynamics of systems consisting of a large or infinite number of entities, in which the mechanism of evolution is random and follows simple, local rules.
The topic had its beginnings in the 70s and 80s, motivated by Statistical Physics and fundamental problems from Probability Theory. It has since developed into a fruitful source of interesting mathematical questions and a very successful framework to model emerging collective complex behavior for systems in a variety of fields, including Biology, Economics and Social Sciences.
The field is sufficiently diverse that there are sub- communities that approach it from very different perspectives. We have identified three broad lines of interest –duality, scaling limits and invariant measures– and have used these to guide selection of speakers. Our goal is to provide an occasion for exchange of experiences and perspectives for young researchers in an immersive week.
Sponsors
Organizers
Conrado da Costa | Durham University |
Richard Kraaij | TU Delft |
Federico Sau | IST Austria, Klosterneuburg |
Daniel Valesin | Groningen University |
Scientific Advisor | |
Remco van der Hofstad | TU Eindhoven |
Speakers
Mini-courses
Patricia Gonçalves | IST Lisbon |
Jan Swart | Czech Academy of Science |
Cristina Toninelli | Paris Dauphine |
Overview Lectures
Pablo Ferrari | UBA Buenos Aires |
Frank Redig | TU Delft |
Invited Talks
Marton Balazs | Bristol University |
Oriane Blondel | Université Lyon 1 |
Peter Mörters | Bath University |
Tom Mountford | EPFL |
Ellen Saada | Université de Paris |
Alexandre Stauffer | Università Roma Tre |
Short Talks
Luisa Andreis | Università degli Studi di Firenze |
Leandro Chiarini | IMPA/Utrecht University |
Simone Floreani | TU Delft |
Chiara Franceschini | IST Lisbon |
Bart van Ginkel | TU Delft |
Jessica Jay | University of Bristol |
Shubamoy Nandam | Leiden University |
Assaf Shapira | Roma Tre University |
Réka Szabó | Université Paris Dauphine |
Siamak Taati | American University of Beirut |
Mario Ayala Valenzuela | |
Clare Wallace | University of Durham |
Programme
T.b.a.
Poster session
For participants, who would like to present a poster, we will organize a poster session.
If you are interested, please send title and abstract of your poster to koorn@eurandom.tue.nl. Deadline for submission is July 31st.
The organizers will review the entries and decide which posters will be accepted for the session.
Abstracts
Queues, stationarity, and stabilisation of last passage percolation
Take a point x on the 2-dimensional integer lattice and another one y North-East from the first. Place i.i.d. Exponential weights on the vertices of the lattice; the last passage time between the two points is the maximal sum of these weights which can be collected by a path that takes North and East steps. The process of these weights as y varies is a difficult one, but locally has a nice asymptotic structure. I'll explain what stationary queues have to do with this and how this insight gives coalescence properties of the maximal-weight paths of last passage.
(joint work with Ofer Busani and Timo Seppäläinen)
(q-)Orthogonal dualities for (a-)symmetric particle systems
In this talk I will show a technique to find duality for those particle systems for which have a reversible measure on $\mathbb{Z}$ and allow an algebraic description.
This work for symmetric and asymmetric processes and relies of the algebraic description of the model. To be concrete I will do the comparison between a simple symmetric exclusion process and its asymmetric version.
The analysis will lead to a family of Krawtchouk polynomials in the symmetric case and their q-analogues in the asymmetric case.
Percolation phase transition in weight-dependent random connection models
We investigate spatial random graphs defined on the points of a Poisson process in d-dimensional space, which combine scale-free degree distributions and long-range effects. Every Poisson point is assigned an independent weight. Given the weight and position of the points, we form an edge between any pair of points independently with a probability depending on the two weights of the points and their distance. Preference is given to short edges and connections to vertices with large weights. We characterize the parameter regime where there is a nontrivial percolation phase transition and show that it depends not only on the power-law exponent of the degree distribution but also on a geometric model parameter. Based on joint work with Peter Gracar and Lukas Lüchtrath.
The Invariance principle for Recurrent Markov Cookie Random walks
We show that in the recurrent case, when diffusively rescaled, the Markov cookie process converges in law to a Brownian motion perturbed at extremities. The key idea is to consider a coarse graining of the process and to appeal to ray Knight theorems.
(joint work with E. Kosygina and J. Peterson)
Diffusive scaling of the Kob-Andersen model
The Kob-Andersen model is an interacting particle system on the lattice, in which sites can contain at most one particle. Each particle is allowed to jump to an empty neighboring site only if there are sufficiently many empty sites in its neighborhood. This way, when the density is very high, the time it takes for the system to evolve is very long. We will see that the system still scales diffusively, but with a coefficient which decays extremely fast as the density increases.
Positive-rate interacting particle systems with Bernoulli invariant measures
Every positive-rate finite-range interacting particle system (in discrete/continuous time) that has a Bernoulli invariant measure is ergodic. The proof is via the entropy method, but unlike the usual entropy arguments, does not require shift-invariance of the starting measure. Two new (?) ingredients are a sharp bound on the entropy increase and a "bootstrap" argument. As an application, this result imposes a sever limitation on the computation power of reversible cellular automata in presence of noise.
(joint work Irène Marcovici)
Registration