FINAL PUBLIC ORAL EXAMINATION OF Aurelien Gribinski

Mon, May 16, 2022, 10:00 am

Rectangular Finite Free Probability Theory  

We study a new type of polynomial convolution that serves as the foundation for building what we call rectangular finite free probability theory, generalizing the square finite free probability theory of Marcus, Spielman and Srivastava. We relate this operation to large rectangular random matrices and explain how it acts on singular values of rectangular matrices in a canonical way. Furthermore, we obtain nontrivial inequalities on roots of polynomials and build some appropriate tools, e.g. the analogue of the classical R-transforms. These developments are inspired by well-known results and concepts from probability theory. We also show that classical orthogonal polynomials such as Gegenbauer or Laguerre polynomials naturally arise through this convolution. Consequently, we deduce new nontrivial properties about the positions of the roots of these polynomials. As an application, we give an elegant proof of the existence of biregular bipartite Ramanujan graphs.

An electronic copy of the dissertation is available per request. Please email bwysocka@princeton.edu if you wish to receive it. 

Zoom available per request: email bwysocka@princeton.edu

 

Location: 
Virtual
Speaker(s): 
Event category: 

Upcoming Events

ANALYSIS OF FLUIDS AND RELATED TOPICS: Turbulent solutions of fluid equations: Alexey Cheskidov, University of Illinois at Chicago

PACM Colloquium, Prof. Lin Lin, UC Berkeley University

Mon, Feb 6, 2023, 4:30 pm
Location: 214 Fine Hall

ANALYSIS OF FLUIDS AND RELATED TOPICS: Kevin Zumbrun, Indiana University

Thu, Feb 9, 2023, 3:00 pm
Location: Fine Hall 314