Related papers: Spatial Brownian motion in renormalized Poisson po…

We discuss the dynamics of a Brownian particle under the influence of a spatially periodic noise strength in one dimension using analytical theory and computer simulations. In the absence of a deterministic force, the Langevin equation can…

We complete the analysis of the phase diagram of the complex branching Brownian motion energy model by studying Phases I, III and boundaries between all three phases (I-III) of this model. For the properly rescaled partition function, in…

In this paper, we are interested in some questions of Greven and den Hollander about the rate function $I\_{\eta}^q$ of quenched large deviations for random walk in random environment. By studying the hitting times of RWRE, we prove that in…

Let $T_{c,\beta}$ denote the smallest $t\ge1$ that a continuous, self-similar Gaussian process with self-similarity index $\alpha>0$ moves at least $\pm c t^\beta$ units. We prove that: (i) If $\beta>\alpha$, then $T_{c,\beta}=\infty$ with…

We consider the 3D incompressible Euler equations in bounded domains $\Omega$ with smooth boundary $\partial\Omega$. Based on the paper by Iwabuchi, Matsuyama and Taniguchi (2019), we define the Besov space $B^s_{p, q}(A)$ by means of the…

In this paper we study the maximal position process of branching Brownian motion in random spatial environment. The random environment is given by a process $\xi = \left(\xi(x)\right)_{x\in\mathbb{R}}$ satisfying certain conditions. We show…

We study a model of $ N $ mutually repellent Brownian motions under confinement to stay in some bounded region of space. Our model is defined in terms of a transformed path measure under a trap Hamiltonian, which prevents the motions from…

We study a continuous-space version of the totally asymmetric simple exclusion process (TASEP), consisting of interacting Brownian particles subject to a driving force in a periodic external potential. Particles are inserted at the leftmost…

We study exclusion processes on the integer lattice in which particles change their velocities due to stickiness. Specifically, whenever two or more particles occupy adjacent sites, they stick together for an extended period of time, and…

We study the behaviour of two Brownian particles coupled by an elastic harmonic force in a quenched disordered medium. We found that to first order in disorder strength, the relative motion weakens (with respect to the reference state of a…

Let B_t^H be a d-dimensional fractional Brownian motion with Hurst parameter H\in(0,1). Assume d\geq2. We prove that the renormalized self-intersection local time\ell=\int_0^T\int_0^t\delta(B_t^H-B_s^H) ds dt -E\biggl(\int_0^T\int_0^t\delta…

Consider a negatively drifted one dimensional Brownian motion starting at positive initial position, its first hitting time to 0 has the inverse Gaussian law. Moreover, conditionally on this hitting time, the Brownian motion up to that time…

We consider an infinite system of Brownian motions which interact through a given Brownian motion being reflected from its left neighbor. Earlier we studied this system for deterministic periodic initial configurations. In this contribution…

We investigate a system of Brownian particles weakly bound by attractive parity-symmetric potentials that grow at large distances as $V(x) \sim |x|^\alpha$, with $0 < \alpha < 1$. The probability density function $P(x,t)$ at long times…

We study the dynamics of a system of $N$ interacting bosons in a disc-shaped trap, which is realised by an external potential that confines the bosons in one spatial dimension to a region of order $\varepsilon$. The interaction is…

We derive a three-term asymptotic expansion for the expected lifetime of Brownian motion and for the torsional rigidity on thin domains in R^n, and a two-term expansion for the maximum (and corresponding maximizer) of the expected lifetime.…

We investigate the three-dimensional motion of a test particle in the gravitational field generated by a non-spherical compact object endowed with a mass quadrupole moment, described by the Erez-Rosen metric, and a radiation field,…

This paper provides a multivariate extension of Bertoin's pathwise construction of a L\'evy process conditioned to stay positive/negative. Thus obtained processes conditioned to stay in half-spaces are closely related to the original…

We study the maximum of Branching Brownian motion (BBM) with branching rates that vary in space, via a periodic function of a particle's location. This corresponds to a variant of the F-KPP equation in a periodic medium, extensively studied…

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…