School on Stochastic interacting particle systems and random matrices

 The School on Stochastic interacting particle systems and random matrices will be held between 16-20 June 2025 at the main lecture hall of the Rényi Institute (Budapest) as part of the thematic semester Probability and Statistical Physics (Jan-June 2025) hosted by the Erdős Center. Graduate students (MSc and PhD), postdocs, and early career researchers are encouraged to apply. Six minicourses are delivered by distinguished researchers of the field consisting of three lectures and one tutorial session of 50 minutes each and a limited number of participants can give a short presentation.

Minicourses

• Charles Bordenave
• Ivan Corwin: The scaling limit of colored ASEP 
  Abstract: I will describe how the Yang-Baxter equation and machinery of Gibbsian line ensembles provides a systematic root to extract the full space-time scaling limit of the colored asymmetric simple exclusion process and its close relatively, the colored stochastic six vertex model. This is based on joint work with Amol Aggarwal and Milind Hegde.
• László Erdős
• Nina Gantert: Exclusion processes: classical results and new questions
  Abstract: We introduce exclusion processes on infinite and (sequences of) finite graphs, both in the symmetric and the asymmetric case. We address questions about the equilibrium distributions and their properties. We explain some results about the rate of convergence to equilibrium in the finite case. We also treat old and recent results about the the speed of a tagged particle in exclusion processes on infinite graphs. No prerequisites are needed, and there will be a focus on open problems.
• Alice Guionnet: CLT and loop equations for Beta-ensembles
  Abstract: The study of global fluctuations in random matrices or Beta-ensembles requires the development of new tools due to the strong correlations of the eigenvalues. One of these is based on the analysis of so-called loop (or Dyson-Schwinger) equations. In this course, we will first recall how to use this approach to analyze (real) Beta-ensembles, following the work of Johansson and G-Borot. We will then discuss how this approach can be generalized to Beta-ensembles through the so-called Nekrasov equations, as introduced in joint work with Borodin and Gorin. Finally, we will discuss more recent developments such as tilings with not simply connected domains and complex potentials.
• Bálint Virág

Application

The application is now open. The application deadline is 15 March 2025. Applicants are asked to send their application to the e-mail address probstatphys25@renyi.hu. The subject of the application e-mail should be "School on IPS and RMT application". The application e-mail should contain the full name, affiliation, and CV (which includes the list of publications).

The school covers full lodging for all accepted international participants (junior participants might share a room with another participant). Please indicate in the application e-mail if lodging in Budapest is requested. MSc and PhD students applying for the school should also ask their supervisor to send a short recommendation e-mail (typically a few informal sentences) to the same contact e-mail address.

A limited number of participants will get a chance to give a short talk about their work. If you would like to give a short talk, please provide the proposed title and abstract in your application e-mail.

Financial support

There is very limited funding for travel support. Participants can apply for travel support in their application e-mail by adding a short explanation about the reason for lacking travel funding and how participation in this school would be beneficial for them.