Related papers: On the singular values of complex matrix Brownian …
We offer an alternative viewpoint on Dyson's original paper regarding the application of Brownian motion to random matrix theory (RMT). In particular we show how one may use the same approach in order to study the stochastic motion in the…
It is well known that upward conditioned Brownian motion is a three-dimensional Bessel process, and that a downward conditioned Bessel process is a Brownian motion. We give a simple proof for this result, which generalizes to any continuous…
Flip-flop processes refer to a family of stochastic fluid processes which converge to either a standard Brownian motion (SBM) or to a Markov modulated Brownian motion (MMBM). In recent years, it has been shown that complex distributional…
We propose an approach to compute the boundary crossing probabilities for a class of diffusion processes which can be expressed as piecewise monotone (not necessarily one-to-one) functionals of a standard Brownian motion. This class…
This paper is a natural continuation of [8], where strong Markov processes are constructed in time inhomogeneous setting with Borel measurable uniformly bounded and uniformly nondegenerate diffusion and drift in $L_{d+1}(\mathbb{R}^{d+1})$.…
Starting with a Brownian motion, we define and study a novel diffusion process by combining stickiness and oscillation properties. The associated stochastic differential equation, resolvent and semigroup are provided. Also the trivariate…
We show in detail some results, outlined in a previous paper regarding the case of Brownian motion (BM), about the distribution of the $n$th-passage time of a one-dimensional diffusion obtained by a space or time transformation of BM,…
Using the Fokker-Planck equation describing the evolution of the transmission eigenvalues for Dyson's Brownian motion ensemble, we calculate the magnetoconductance of a ballistic chaotic dot in in the crossover regime from the orthogonal to…
We consider a Markov-modulated Brownian motion reflected to stay in a strip [0,B]. The stationary distribution of this process is known to have a simple form under some assumptions. We provide a short probabilistic argument leading to this…
We develop a unifying theory for four different objects: (1) infinite systems of interacting massive particles; (2) solutions to the Dean-Kawasaki equation with singular drift and space-time white noise; (3) Wasserstein diffusions with a.s.…
We propose a new classification scheme for diffusion processes for which the backward Kolmogorov equation is solvable in analytically closed form by reduction to hypergeometric equations of the Gaussian or confluent type. The construction…
We present a study on the dynamics of a system consisting of a pair of hardcore particles diffusing with different rates. We solved the drift-diffusion equation for this model in the case when one particle, labeled F, drifts and diffuses…
We consider several critical wetting models. In the discrete case, these probability laws are known to converge, after an appropriate rescaling, to the law of a reflecting Brownian motion, or of the modulus of a Brownian bridge, according…
We construct a class of superprocesses by taking the high density limit of a sequence of interacting-branching particle systems. The spatial motion of the superprocess is determined by a system of interacting diffusions, the branching…
We consider in this work a one parameter family of hypoelliptic diffusion processes on the unit tangent bundle $T^1 \mathcal M$ of a Riemannian manifold $(\mathcal M,g)$, collectively called kinetic Brownian motions, that are random…
The Ray--Knight theorems show that the local time processes of various path fragments derived from a one-dimensional Brownian motion $B$ are squared Bessel processes of dimensions $0$, $2$, and $4$. It is also known that for various…
We analyze quantal Brownian motion in $d$ dimensions using the unified model for diffusion localization and dissipation, and Feynman-Vernon formalism. At high temperatures the propagator possess a Markovian property and we can write down an…
Starting from the Gisin-Percival state diffusion equation for the pure state trajectory of a composite bipartite quantum system and exploiting the purification of a mixed state via its Schmidt decomposition, we write the diffusion equation…
We consider the system of one-sided reflected Brownian motions which is in variational duality with Brownian last passage percolation. We show that it has integrable transition probabilities, expressed in terms of Hermite polynomials and…
The stochastic trajectories of molecules in living cells, as well as the dynamics in many other complex systems, often exhibit memory in their path over long periods of time. In addition, these systems can show dynamic heterogeneities due…