Communication protocols and spectral gap estimates in models of collective dynamics
数学专题报告
报告题目(Title)：Communication protocols and spectral gap estimates in models of collective dynamics
报告人(Speaker)：Prof. Roman Shvydkoy (University of Illinois at Chicago)
地点(Place)：Zoom ID: 844 926 12193 | Password: 123456
时间(Time)：2026年6月25日（周四）9:00-10:00
邀请人(Inviter)：薛留堂
报告摘要
We will describe a new framework based around the concept of a communication protocol that encapsulates many classical alignment models including Cucker-Smale, Motsch-Tadmor, and others. The framework allows to state general existence and renormalization results for weak solutions of the associated Fokker-Planck models, justify mean-field, hydrodynamic limits, etc. Specifically for the so-called conservative protocols -- under which the total momentum of the system is conserved -- we prove an estimate on the spectral gap of the alignment operator which depends only on the local thickness of the flock. As an application of these estimates, we demonstrate relaxation of weak solutions to the kinetic system for arbitrary large data.
