[Probabilidad-Estadistica-Seminario] Charla en FING: Generalized Limit Theorem for strongly correlated variables

[Ernesto Mordecki]

Hola, para difundir la siguiente actividad:

Próxima semana: Martes 7 de marzo 11hs en sala de seminarios del IF de FING

Expositor: Bertrand Delamotte

Título: Generalized Limit Theorem for strongly correlated variables: the 
probability distribution of the order parameter of the Ising model from 
the functional renormalization group

Resumen: The central limit theorem states that the probability 
distribution function (PDF) of the sum of independent and identically 
distributed random variables becomes gaussian when the number of 
variables goes to infinity. It has been a long-standing problem to 
generalize this theorem when the variables are no longer independent and 
especially when they are strongly correlated. In physics, such a 
situation is encountered in the vicinity of a second order phase 
transition. On the example of the Ising model in three dimensions, we 
show that the functional nonperturbative renormalization group is the 
proper tool to address this problem. We show that the simplest 
implementation, that is, the crudest approximation scheme of the 
functional renormalization group à la Wilson allows for a quantitative 
determination of the family of universal critical PDFs of the order 
parameter (the magnetization). At the conceptual level, this study 
bridges the gap between probability theory and the renormalization group.

Ref: "Critical probability distributions of the order parameter from the 
functional renormalization group", I. Balog, A. Rançon, B. Delamotte, 
Phys. Rev. Lett. 129, 210602 (2022)

saludos
Ernesto
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