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Diffusion with stochastic resetting.
We study simple diffusion where a particle stochastically resets to its initial position at a constant rate r. A finite resetting rate leads to a nonequilibrium stationary state with non-Gaussian
Extreme value statistics of eigenvalues of Gaussian random matrices.
  • D. Dean, S. Majumdar
  • Mathematics
    Physical review. E, Statistical, nonlinear, and…
  • 11 January 2008
TLDR
The density of states in Gaussian ensembles whose eigenvalues are restricted to lie in the interval [zeta1,zeta2] is obtained, thus generalizing the celebrated Wigner semi-circle law to these restricted ensemble.
Height correlations in the Abelian sandpile model
The authors study the distribution of heights in the self-organized critical state of the Abelian sandpile model on a d-dimensional hypercubic lattice. They calculate analytically the concentration
Large deviations of extreme eigenvalues of random matrices.
TLDR
The average density of states in matrices whose eigenvalues are restricted to be larger than a fixed number zeta is calculated, thus generalizing the celebrated Wigner semicircle law.
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
Brownian Functionals in Physics and Computer Science
TLDR
This article provides a pedagogical introduction to the path integral methods leading to the derivation of the celebrated Feynman-Kac formula.
Persistence in nonequilibrium systems
TLDR
Some recent theoretical efforts in calculating this nontrivial exponent in various models are reviewed and some recent experiments that measured this exponent are mentioned, mentioning the emerging new directions towards different generalizations of persistence.
Diffusion with optimal resetting
We consider the mean time to absorption by an absorbing target of a diffusive particle with the addition of a process whereby the particle is reset to its initial position with rate r. We consider
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