Condensation transition in large deviations of self-similar Gaussian processes with stochastic resetting

We study the fluctuations of the area A(t)=integral 0tx(tau)d tau x(tau) with Hurst exponent H > 0 (e.g., standard or fractional Brownian motion, or the random acceleration process) that stochastically resets to the origin at rate r. Typical fluctuations of A(t) scale as similar to t t and on this scale the distribution is Gaussian, as one would expect from the central limit theorem. Here our main focus is on atypically large fluctuations of A(t). In the long-time limit t -> infinity, we find that the full distribution of the area takes the form PrAt similar to exp-t alpha phi(>A/t beta alpha = 1/(2H + 2) and beta = (2H + 3)/(4H + 4) in the regime of moderately large fluctuations, and a different anomalous scaling form Pr(>At similar to exp-t psi(>A/t(>2H+3/2 At

Automated summary

This paper investigates the fluctuations of the area A(t) with Hurst exponent H > 0 (e.g., standard or fractional Brownian motion, or the random acceleration process). It is found that in the long-time limit, the distribution of A(t) takes on a non-Gaussian form with different anomalous scaling.