SPP 2265 - Subproject: The Heat Flow of Random Polynomials

Basic data for this project

Type of projectSubproject in DFG-joint project hosted outside University of Münster
Duration at the University of Münster01/04/2024 - 31/01/2025 | 1st Funding period

Description

The main goal of this project is to analyze the evolution of the point process of zeros of random polynomials as these undergo the heat flow. The problem belongs to an active line of research studying how differential operators acting on random functions affect their zeros. Even though the problem seems innocent at first glance, this project is rich of fascinating phenomena and features surprising links to other areas, like random matrix theory, free probability, (optimal) transport, differential equations and complex analysis that we shall explore and utilize. Initiated by the desire to connect the circular law, elliptic law and semicircle law from random matrix theory via a dynamic of the eigenvalues and as a push-forward under a transport map, we study the corresponding problem for the zeros of random polynomials with independent coefficients as they undergo the heat flow. Core questions are: 1) How does the geometry of the limiting (as the degree tends to infinity) zero distribution with the heat flow? 2) Is it possible to establish (global) universality for the limiting distribution? 3) What can we say about the dynamics of individual zeros or about the microscopic point process after the heat flow? 4) Does the theory extend to other differential operators and other models of (random) functions?

Keywordszufällige Polynome
DFG-Gepris-IDhttps://gepris.dfg.de/gepris/projekt/531561854
Funding identifierJA 3563/1-1 | DFG project number: 531561854
Funder / funding scheme
  • DFG - Priority Programme (SPP)

Project management at the University of Münster

Jalowy, Jonas
Professorship of applied mathematics

Applicants from the University of Münster

Jalowy, Jonas
Professorship of applied mathematics

Coordinating organisations outside the University of Münster

  • Weierstrass Institute for Applied Analysis and Stochastics (WIAS)Germany