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UID:20250729T180950EDT-9939LjSNsz@132.216.98.100
DTSTAMP:20250729T220950Z
DESCRIPTION:CRM-ISM Probability Seminar\n\nTitle: Stochastic PDE as scaling
  limits of interacting particle systems\n\nAbstract: \n\nInteracting parti
 cle models are often employed to gain understanding of the emergence of ma
 croscopic phenomena from microscopic laws of nature. These individual-base
 d models capture fine details\, including randomness and discreteness of i
 ndividuals\, that are not considered in continuum models such as partial d
 ifferential equations (PDE) and integral-differential equations. The chall
 enge is how to simultaneously retain key information in microscopic models
  as well as efficiency and robustness of macroscopic models. In this talk\
 , I will discuss how this challenge can be overcome by elucidating the pro
 babilistic connections between particle models and PDE. These connections 
 also explain how stochastic partial differential equations (SPDE) arise na
 turally under a suitable choice of level of detail in modeling complex sys
 tems. I will also present some novel scaling limits including SPDE on grap
 hs and coupled SPDE. These SPDE not only interpolate between particle mode
 ls and PDE\, but also quantify the source and the order of magnitude of st
 ochasticity. Scaling limit theorems and new duality formulas are obtained 
 for these SPDE\, which connect phenomena across scales and offer insights 
 about the genealogies and the time-asymptotic properties of the underlying
  population dynamics.\n\nReferences:\n\n1. Genealogies in expanding popula
 tions. With Rick Durrett. Annals of Applied Probability. Vol. 26 (6)\, 345
 6-3490\, 2016.\n\n2. Stochastic PDEs on graphs as scaling limits of discre
 te interacting systems. To appear in Bernoulli.\n\n3. Wave propagation for
  reaction-diffusion equations on infinite trees. With Wenqing Hu and Grigo
 ry Terlov. Under review.\n\n \n\nLink: https://mcgill.zoom.us/j/8759669467
 2?pwd=VG5WZjllUFdQVWxjN29rV2RMZDFlUT09\n\nMeeting ID: 875 9669 4672\n\nPas
 scode: problab\n\n \n\n \n
DTSTART:20210324T170000Z
DTEND:20210324T180000Z
SUMMARY:Louis Fan (Indiana)
URL:/mathstat/channels/event/louis-fan-indiana-327895
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