The run-and-tumble particle: from universal properties to nonequilibrium phase transitions

In this talk, I will present recent results on the statistical properties of active particles. I will focus on the run-and-tumble particle (RTP) model, which describes the persistent motion of a class of bacteria, including E. coli. In the first part of the talk, I will show that many properties of this model, including the survival probability and the record statistics, are universal, i.e., independent of the system's dimension and the speed fluctuations of the particle. In the second part of the talk, I will investigate the position distribution of a single RTP at late times. I will show that, under certain conditions, a condensation transition can be observed in the large-deviation regime where the particle is far from its starting position.

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