Statut  Confirmé 
Série  SEMLPTMC 
Domaines  condmat.meshall 
Date  Jeudi 23 Janvier 2020 
Heure  14:00 
Institut  LPTMC 
Salle  Jussieu tower 1312 5th floor room 523 
Nom de l'orateur  Meerson 
Prenom de l'orateur  Baruch 
Addresse email de l'orateur  
Institution de l'orateur  Racah institue of physics, Hebrew university of Jerusalem, Israël 
Titre  Geometrical optics of constrained Brownian motion: three short stories 
Résumé  The optimal fluctuation method — essentially geometrical optics — gives a deep insight into large deviations of Brownian motion, and it achieves this purpose by simple means. Here we illustrate these points by telling three short stories about Brownian motions, ``pushed" into a largedeviation regime by constraints. Story 1 deals with a longtime survival of a Brownian particle in 1 + 1 dimension against absorption by a wall which advances according to a power law $x_w (t) \sim t^{\gamma}$, where $\gamma> 1/2$. We also calculate the large deviation function (LDF) of the particle position at an earlier time, conditional on the survival by a later time. Story 2 addresses a stretched Brownian motion above an absorbing obstacle in the plane. We compute the shorttime LDF of the position of the surviving Brownian particle at an intermediate point. In story 3 we compute the shorttime LDF of the winding angle of a Brownian particle wandering around a reflecting disk in the plane. In all three stories we uncover singularities of the LDFs which can be interpreted as dynamical phase transitions and which have a simple geometric origin. We also use the smalldeviation limit of the geometrical optics to reconstruct the distribution of typical fluctuations. We argue that, in stories 1 and 2, this is the Ferrari–Spohn distribution. The talk is based on a recent paper by B. Meerson and N. R. Smith, J. Phys. A: Math. Theor. 52, 415001 (2019) . 
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