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Seminars

Analysis Seminar

Quantitative Flocking in Delayed Stochastic Cucker–Smale Systems

2026/09/29 (Tue.) 10:00~13:00
  • Date : 2026/09/29 (Tue.) 10:00~13:00
  • Location : online
  • Speaker : Fanqin Zeng (Seoul National University)
  • Organizer : Tai-Ping Liu (AS)
  • Abstract : We study the long-time flocking behavior of a stochastic Cucker–Smale system with time delay and agent-wise independent multiplicative Brownian noise. For the original Cucker–Smale communication kernel with algebraic decay, the main difficulty is that the interaction strength may become arbitrarily weak as particles spread, while the delay destroys the usual monotonicity of the velocity fluctuation. Under suitable moment assumptions on the initial history and sufficiently small delay and noise, we establish N-uniform polynomial decay of the mean-square velocity fluctuation together with uniform-in-time spatial cohesion. For each fixed number of particles, we further obtain almost-sure flocking. Our analysis combines a memory-corrected Lyapunov functional, high-order empirical moment estimates, and a time-varying effective-region argument. Our results provide a positive answer to a question raised by Erban, Haskovec, and Sun concerning flocking for delayed stochastic Cucker–Smale systems with algebraically decaying communication.

Click here to register: https://forms.gle/aYBBzmUwbEWkmBMW6  (Deadline: 4pm, Sep. 28)
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請注意截止時間，逾時不受理報名。Please note the deadline; no applications will be accepted after the deadline.

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