Related papers: Brownian motion on Lie groups and open quantum sys…
Our goal is to find classes of convolution semigroups on Lie groups $G$ that give rise to interesting processes in symmetric spaces $G/K$. The $K$-bi-invariant convolution semigroups are a well-studied example. An appealing direction for…
Brownian motion is modelled by a harmonic oscillator (Brownian particle) interacting with a continuous set of uncoupled harmonic oscillators. The interaction is linear in the coordinates and the momenta. The model has an analytical solution…
Quantum mechanics can be formulated in terms of phase-space functions, according to Wigner's approach. A generalization of this approach consists in replacing the density operators of the standard formulation with suitable functions, the…
We consider quantum random walks in an infinite-dimensional phase space constructed using Weyl representation of the coordinate and momentum operators in the space of functions on a Hilbert space which are square integrable with respect to…
Consider a sequence of n bi-infinite and stationary Brownian queues in tandem. Assume that the arrival process entering in the first queue is a zero mean ergodic process. We prove that the departure process from the n-th queue converges in…
This paper considers a classical question of approximation of Brownian motion by a random walk in the setting of a sub-Riemannian manifold $M$. To construct such a random walk we first address several issues related to the degeneracy of…
In systems possessing spatial or dynamical symmetry breaking, Brownian motion combined with symmetric external input signals, deterministic or random, alike, can assist directed motion of particles at the submicron scales. In such cases,…
A unitary representation of a, possibly infinite dimensional, Lie group $G$ is called semi-bounded if the corresponding operators $i\dd\pi(x)$ from the derived representations are uniformly bounded from above on some non-empty open subset…
We define a new diffusive matrix model converging towards the $\beta$ -Dyson Brownian motion for all $\beta\in [0,2]$ that provides an explicit construction of $\beta$-ensembles of random matrices that is invariant under the…
We propose a bivariate model for a pair of dependent unit vectors which is generated by Brownian motion. Both marginals have uniform distributions on the sphere, while the conditionals follow so-called ``exit'' distributions. Some…
This paper describes the quality of convergence to an infinitely divisible law relative to free multiplicative convolution. We show that convergence in distribution for products of identically distributed and infinitesimal free random…
The classical theorem by Pitman states that a Brownian motion minus twice its running infimum enjoys the Markov property. On the one hand, Biane understood that Pitman's theorem is intimately related to the representation theory of the…
The main objective of this paper consists in creating a new class of copulae from various joint distributions occurring in connection with certain Brownian motion processes. We focus our attention on the distributions of univariate Brownian…
We consider certain questions pertaining to noncommutative generalized Brownian motions with multiple processes. We establish a framework for generalized Brownian motion with multiple processes similar to that defined by Guta and prove…
Structures of quantum Fokker-Planck equations are characterized with respect to the properties of complete positivity, covariance under symmetry transformations and satisfaction of equipartition, referring to recent mathematical work on…
Overdamped Brownian motion of a self-propelled particle is studied by solving the Langevin equation analytically. On top of translational and rotational diffusion, in the context of the presented model, the "active" particle is driven along…
The theory of quantum dynamical semigroups within the mathematically rigorous framework of completely positive dynamical maps is reviewed. First, the axiomatic approach which deals with phenomenological constructions and general…
We analyze the microscopic model of quantum Brownian motion, describing a Brownian particle interacting with a bosonic bath through a coupling which is linear in the creation and annihilation operators of the bath, but may be a nonlinear…
Motivated by quantum information theory, we introduce a dynamical random state built out of the sum of $k \geq 2$ independent unitary Brownian motions. In the large size limit, its spectral distribution equals, up to a normalising factor,…
We begin with a review and analytical construction of quantum Gaussian process (and quantum Brownian motions) in the sense of [25],[10] and others, and then formulate and study in details (with a number of interesting examples) a definition…