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Persistence and first-passage properties in nonequilibrium systems
In this review, we discuss the persistence and the related first-passage properties in extended many-body nonequilibrium systems. Starting with simple systems with one or few degrees of freedom, such
Stochastic resetting and applications
In this Topical Review we consider stochastic processes under resetting, which have attracted a lot of attention in recent years. We begin with the simple example of a diffusive particle whose
Top eigenvalue of a random matrix: large deviations and third order phase transition
We study the fluctuations of the largest eigenvalue ?max of N ? N random matrices in the limit of large N. The main focus is on Gaussian ? ensembles, including in particular the Gaussian orthogonal
Collective dynamics of social annotation
It is shown that the process of social annotation can be seen as a collective but uncoordinated exploration of an underlying semantic space, pictured as a graph, through a series of RWs.
Dynamical transition in the temporal relaxation of stochastic processes under resetting.
It is shown that as time progresses an inner core region around the resetting point reaches the steady state, while the region outside the core is still transient, and the boundaries of the core region grow with time as power laws at late times with new exponents.
Real Roots of Random Polynomials and Zero Crossing Properties of Diffusion Equation
AbstractWe study various statistical properties of real roots of three different classes of random polynomials which recently attracted a vivid interest in the context of probability theory and
Noninteracting fermions at finite temperature in a d -dimensional trap: Universal correlations
We study a system of $N$ non-interacting spin-less fermions trapped in a confining potential, in arbitrary dimensions $d$ and arbitrary temperature $T$. The presence of the trap introduces an edge
Exact Persistence Exponent for the 2D-Diffusion Equation and Related Kac Polynomials.
It is shown that the probability q_{0}(n) that Kac's polynomials, of (even) degree n, have no real root decays, for large n, as q¬0 (n)∼n^{-3/4}.
Number statistics for β-ensembles of random matrices: Applications to trapped fermions at zero temperature.
Analytical results are presented for the full counting statistics of zero-temperature one-dimensional spinless fermions in a harmonic trap and generically the number variance var(N_{I}) exhibits a nonmonotonic behavior as a function of the size of the interval.