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UID:20250712T155127EDT-8087hdtugK@132.216.98.100
DTSTAMP:20250712T195127Z
DESCRIPTION:Title: Hydrodynamic limit large deviation for stochastic Carlem
 an particles\, a Hamilton-Jacobi approach\n\nAbstract: The deterministic C
 arleman equation can be considered as an one dimensional two speed fictiti
 ous gas model. Its associated hydrodynamic limit gives a nonlinear heat eq
 uation. The first rigorous derivation of such limit was given by Kurtz in 
 1973. In this talk\, starting from a more refined stochastic model giving 
 the Carleman equation as the mean field\, we derive a macroscopic fluctuat
 ion structure associated with the hydrodynamic limit.\n	\n	The large deviati
 on result is established through an abstract Hamilton-Jacobi method applie
 d to this specific setting. The principal idea is to identify a two scale 
 averaging structure in the context of Hamiltonian convergence in the space
  of probability measures. This is conceptually achieved through a change o
 f coordinate to the density-flux description of the problem. We also exten
 d a method in the weak KAM theory to the infinite particle context for exp
 licitly identifying the effective Hamiltonian. In the end\, we conclude by
  establishing a comparison principle for a set of Hamilton-Jacobi equation
 s in the space of measures.\n	\n	I will present some subtle issues involved 
 and put the method into perspective regarding challenges we face when appl
 ying to other hydrodynamic issues.\n	\n	This is a joint work with Toshio Mik
 ami and Johannes Zimmer.\n
DTSTART:20191204T200000Z
DTEND:20191204T210000Z
LOCATION:Room 1205\, Burnside Hall\, CA\, QC\, Montreal\, H3A 0B9\, 805 rue
  Sherbrooke Ouest
SUMMARY:Jin Feng (University of Kansas)
URL:/mathstat/channels/event/jin-feng-university-kansa
 s-302938
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