Amol Aggarwal (Stanford University)
Many Body Asymptotics for the Toda Lattice abstract
Abstract:
The Toda lattice prescribes the evolution of many particles interacting under certain Hamiltonian dynamics; it is an archetypal example of a completely integrable system. In this talk we describe several results providing the long-time asymptotics of this system, under random, dense initial data. The proofs proceed by finding a way to interpret the Toda lattice as a collection of "quasi-particles" that behave similarly to solitons, and providing a framework to study how these quasi-particles asymptotically evolve in time. The arguments use ideas from random matrix theory, particularly the analysis of Lyapunov exponents governing the decay rates of eigenvectors of random tridiagonal matrices.
16:30 • UZH Zentrum, Building KO2, Room F 150