Status  Confirmed 
Seminar Series  SEMLPTMC 
Subjects  condmat.meshall 
Date  Thursday 23 January 2020 
Time  14:00 
Institute  LPTMC 
Seminar Room  Jussieu tower 1312 5th floor room 523 
Speaker's Last Name  Meerson 
Speaker's First Name  Baruch 
Speaker's Email Address  
Speaker's Institution  Racah institue of physics, Hebrew university of Jerusalem, Israël 
Title  Geometrical optics of constrained Brownian motion: three short stories 
Abstract  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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