Condensation transition in large deviations of the Ornstein-Uhlenbeck process and of reset fractional Brownian motion

I will present recent results for two problems related to stochastic dynamics:

(i) the full distribution of the time integral of the nth moment of an Ornstein-Uhlenbeck process.

(ii) the full distribution of the mean position of a fractional Brownian motion with stochastic resetting to the origin.

We find that both in problem (i) for n>2, and in problem (ii), the long-time scaling form of the distribution obey large-deviation principles with anomalous exponents (i.e., the exponents are not equal to 1).

The rate functions, that we calculate exactly, exhibit first-order dynamical phase transitions which separate between a homogeneous phase that describes the Gaussian distribution of typical fluctuations, and a "condensed" phase that describes the tails of the distributions.

Remarkably, the anomalous exponents and the rate functions are identical for the two problems, up to scaling factors.

The talk is based on the two recent papers:

N. R. Smith, Phys. Rev. E 105, 014120 (2022), and

N. R. Smith and S. N. Majumdar, arXiv:2202.03546

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