Réunion d'été SMC 2025
Ville de Québec, 6 - 9 juin 2025
Stochastic and Singular PDEs, and Related Fields
Org: Damir Kinzebulatov (Université Laval) et Jie Xiao (Memorial University)
Org: Damir Kinzebulatov (Université Laval) et Jie Xiao (Memorial University)
- RALUCA BALAN, Ottawa
- ILIA BINDER, Toronto
- LINAN CHEN, McGill
- YU-TING CHEN, Victoria
- TOMASZ KLIMSIAK, Polish Academy of Sciences
- WEIYANG LI, Memorial
- RAPHAEL MADOU, McGill
- NGUYEN NGUYEN, Memorial
- JANOSCH ORTMANN, UQAM
- ZACHARY SELK, Queen's University
Onsager-Machlup under Renormalization [PDF]
- ILIA BINDER, Toronto
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Stochastic quantization is a procedure for constructing measures, typically on spaces of distributions, with a given "probability density function" as the invariant measure of a stochastic PDE. These "densities" typically involve nonlinearities of distributions which necessitates renormalization. The renormalization, and the lack of a Lebesgue measure on infinite dimensional spaces leads to the question of in what sense these rigorously constructed measures have the given "density". The Onsager-Machlup function is one rigorous notion of probability density function on infinite dimensional spaces.
We are interested in the $\Phi_d^4$, and related, measures in dimensions $d\leq 3$ arising from EQFT. In dimension $1$, no renormalization is required. In dimension $2$, Wick renormalization is sufficient and in dimension $3$, the theory of regularity structures or paracontrolled calculus can be used to renormalize.
In an ongoing joint work with Ioannis Gasteratos (TU Berlin) we analyze the Onsager-Machlup function of the $\Phi^4$ and related measures.
- SHAHAB SHAABANI, Concordia
- REIHANEH VAFADAR, Laval
- DEPING YE, Memorial
- CHENGJUN YUE, Memorial
- TONG ZHANG, Memorial
- WEI ZHENZHEN, Memorial
- REIHANEH VAFADAR, Laval