Related papers: Area fluctuations on a subinterval of Brownian exc…
Using structures of Abstract Wiener Spaces, we define a fractional Brownian field indexed by a product space $(0,1/2] \times L^2(T,m)$, $(T,m)$ a separable measure space, where the first coordinate corresponds to the Hurst parameter of…
We consider a superprocess with coalescing Brownian spatial motion. We first prove a dual relationship between two systems of coalescing Brownian motions. In consequence we can express the Laplace functionals for the superprocess in terms…
Aiming to understand the distribution of fitness levels of individuals in a large population undergoing selection, we study the particle configurations of branching Brownian motion where each particle independently moves as Brownian motion…
The diffusion of chiral active Brownian particles in three-dimensional space is studied analytically, by consideration of the corresponding Fokker-Planck equation for the probability density of finding a particle at position…
The optimal fluctuation method -- essentially geometrical optics -- gives a deep insight into large deviations of Brownian motion. Here we illustrate this point by telling three short stories about Brownian motions, "pushed" into a…
We explore statistical fluctuations over the ensemble of quantum trajectories in a model of two-dimensional free fermions subject to projective monitoring of local charge across the measurement-induced phase transition. Our observables are…
We consider a planar Brownian loop $B$ that is run for a time $T$ and conditioned on the event that its range encloses the unusually high area of $\pi T^2$, with $T$ being large. We study the deviation of the range of the conditioned…
We present a model of anomalous diffusion consisting of an ensemble of particles undergoing homogeneous Brownian motion except for confinement by randomly placed reflecting boundaries. For power-law distributed compartment sizes, we…
We consider active Brownian particles that intermittently switch between active and inactive states. Such behavior is ubiquitous at all scales, from bacteria to animals and in artificial active systems. We derive exact expressions for key…
The logarithmic correction for the order of the maximum of a two-type reducible branching Brownian motion on the real line exhibits a double jump when the parameters (the ratio of the diffusion coefficients of the two types of particles,…
Drawdowns measuring the decline in value from the historical running maxima over a given period of time, are considered as extremal events from the standpoint of risk management. To date, research on the topic has mainly focus on the side…
This work deals with the overdamped motion of a particle in a fluctuating one-dimensional periodic potential. If the potential has no inversion symmetry and its fluctuations are asymmetric and correlated in time, a net flow can be generated…
Explicit formulae for the densities of the first hitting times to the sphere of Brownian motions with drifts are given. We need to consider the joint distributions of the first hitting times to the sphere and the hitting positions of the…
The motion of overdamped particles in a one-dimensional spatially-periodic potential is considered. The potential is also randomly-fluctuating in time, due to multiplicative colored noise terms, and has a deterministic tilt. Numerical…
We study the Brownian force model (BFM), a solvable model of avalanche statistics for an interface, in a general discrete setting. The BFM describes the overdamped motion of elastically coupled particles driven by a parabolic well in…
A conditional diffusion model has been developed to analyze intricate conductance fluctuations called universal conductance fluctuations or quantum fingerprints appearing in quantum transport phenomena. The model reconstructs impurity…
A system reservoir model, where the associated reservoir is modulated by an external colored random force, is proposed to study the transport of an overdamped Brownian particle in a periodic potential. We then derive the analytical…
In this work exact expressions for the distribution function of the accumulated area swept by reunions and meanders of $N$ vicious Brownian particles up to time $T$ are derived. The results are expressed in terms of a generalised Airy…
Brownian motion in a granular gas in a homogeneous cooling state is studied theoretically and by means of molecular dynamics. We use the simplest first-principle model for the impact-velocity dependent restitution coefficient, as it follows…
We investigate piecewise-linear stochastic models as with regards to the probability distribution of functionals of the stochastic processes, a question which occurs frequently in large deviation theory. The functionals that we are looking…