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Soheli Mukherjee

As seen in: Physical Review B
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Articles

Large deviations in statistics of the local time and occupation time for a run and tumble particle

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By Soheli Mukherjee, Blaustein Institutes, Sede Boqer Campus, Pierre Le Doussal
| Physical Review B
We investigate the statistics of the local time T=∫0Tδ(x(t))dt that a run and tumble particle (RTP) x(t) in one dimension spends at the origin, with or without an external drift. By relating the local time to the number of times the RTP crosses the origin, we find that the local time distribution P(T) satisfies the large deviation principle P(T)∼e−TI(T/T) in the large observation time limit T→∞.
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Dynamical phase transition in the occupation fraction statistics for noncrossing Brownian particles

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By Blaustein Institutes, Naftali Smith, Soheli Mukherjee
| Physical Review B
Abstract We consider a system of N noncrossing Brownian particles in one dimension. We find the exact rate function that describes the long-time large deviation statistics of their occupation fraction in a finite interval in space. Remarkably, we find that, for any general N≥2, the system undergoes N−1 dynamical phase transitions of second order.
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