• Corpus ID: 237439382

Field theory of survival probabilities, extreme values, first passage times, and mean span of non-Markovian stochastic processes

  title={Field theory of survival probabilities, extreme values, first passage times, and mean span of non-Markovian stochastic processes},
  author={Benjamin Walter and Gunnar Pruessner and Guillaume Salbreux},
Benjamin Walter, 2, 3, 4 Gunnar Pruessner, 2 and Guillaume Salbreux 6 Department of Mathematics, Imperial College London, 180 Queen’s Gate, SW7 2AZ London, United Kingdom Centre for Complexity & Networks, Imperial College London, SW7 2AZ London, United Kingdom SISSA-International School for Advanced Studies, via Bonomea 265, 34136 Trieste, Italy INFN, Sezione di Trieste, 34136 Trieste, Italy∗ The Francis Crick Institute, 1 Midland Road, NW1 1AT London, United Kingdom Department of Genetics and… 

Figures from this paper


Volume explored by a branching random walk on general graphs
Analytical results are presented on the scaling of the volume explored by a branching random walk in the critical regime, the onset of epidemics, in general environments, and the spectral properties of real social and metabolic networks.
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
Global Persistence Exponent for Nonequilibrium Critical Dynamics.
It is argued that θ is a new independent exponent, associated with the probability, p(t) ∼ t −θ , that the global order parameter has not changed sign in time t following a quench to the critical point, that is in general a new, non-trivial critical exponent.
A Field-Theoretic Approach to the Wiener Sausage
The Wiener Sausage, the volume traced out by a sphere attached to a Brownian particle, is a classical problem in statistics and mathematical physics. Initially motivated by a range of
AOUP in the presence of Brownian noise: a perturbative approach
By working in the small persistence time limit, we determine the steady-state distribution of an active Ornstein Uhlenbeck particle (AOUP) experiencing, in addition to self-propulsion, a Gaussian
Perturbation theory for fractional Brownian motion in presence of absorbing boundaries.
This work studies x(t) in presence of an absorbing boundary at the origin and focuses on the probability density P(+)(x,t) for the process to arrive at x at time t, starting near the origin at time 0, given that it has never crossed the origin.
Steady state, relaxation and first-passage properties of a run-and-tumble particle in one-dimension
We investigate the motion of a run-and-tumble particle (RTP) in one dimension. We find the exact probability distribution of the particle with and without diffusion on the infinite line, as well as
The entropy production of Ornstein–Uhlenbeck active particles: a path integral method for correlations
By employing a path integral formulation, we obtain the entropy production rate for a system of active Ornstein-Uhlenbeck particles (AOUP) both in the presence and in the absence of thermal noise.
Persistence in nonequilibrium systems
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.
Abstract : The solution to the first passage problem for a strongly continuous temporally homogeneous Markoff process X(t) is given. If T = T sub ab (x) is a random variable giving the time of first