Related papers: The compact support property for the $\Lambda$-Fle…

It has been shown by various authors that the diameter of a given nontrivial bounded connected set $\mathcal{X}$ grows linearly in time under the action of an isotropic Brownian flow (IBF), which has a nonnegative top-Lyapunov exponent. In…

We show that the increments of the KPZ fixed point started from arbitrary initial data are \emph{mutually} absolutely continuous with respect to Brownian motion with diffusion parameter $2$ on compacts, extending the one-sided Brownian…

For every bounded planar domain $D$ with a smooth boundary, we define a `Lyapunov exponent' $\Lambda(D)$ using a fairly explicit formula. We consider two reflected Brownian motions in $D$, driven by the same Brownian motion (i.e., a…

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 establish some scaling limits for a model of planar aggregation. The model is described by the composition of a sequence of independent and identically distributed random conformal maps, each corresponding to the addition of one…

We consider weak non-negative solutions to the stochastic partial differential equation \[ \partial_t Y(t,x) = \Delta Y(t,x) + Y(t,x)^\gamma \dot{L}(t,x), \] for $(t,x) \in \mathbb{R}_+ \times \mathbb{R}^d$, where $\gamma > 0$ and $\dot{L}$…

Taking an open quantum systems approach, we derive a collective equation of motion for the dynamics of a matter-wave bright soliton moving through a thermal cloud of a distinct atomic species. The reservoir interaction involves energy…

In the setting of finite reflection groups, we prove that the projection of a Brownian motion onto a closed Weyl chamber is another Brownian motion normally reflected on the walls of the chamber. Our proof is probabilistic and the…

In this paper we investigate the class of grey Brownian motions $B_{\alpha,\beta}$ ($0<\alpha<2$, $0<\beta\leq1$). We show that grey Brownian motion admits different representations in terms of certain known processes, such as fractional…

We investigate the structural properties of the last passage time $\sigma_z^{\lambda}$ at level $z > 0$ of a Brownian motion with positive drift $\lambda > 0$, denoted $B^{\lambda} = (B_t + \lambda t)_{t \geq 0}$, in the filtration…

In this paper, we determine the Poisson boundary of the relativistic Brownian motion in two classes of Lorentzian manifolds, namely model manifolds of constant scalar curvature and Robertson--Walker space-times, the latter constituting a…

In this paper, we prove the compact support property for a class of nonlinear SPDE including the equation that the density of one-dimensional Super-Brownian Motion in random environment satisfies.

A result of R. Durrett, D. Iglehart and D. Miller states that Brownian meander is Brownian motion conditioned to stay positive for a unit of time, in the sense that it is the weak limit, as $x$ goes to 0, of Brownian motion started at $x>0$…

We prove the strong convergence of the spectrum of the kinetic Brownian motion to the spectrum of base Laplacian for a large class of compact locally Riemannian homogeneous spaces, in particular all compact locally symmetric spaces. This…

Based on analytical and numerical calculations we study the dynamics of an overdamped colloidal particle moving in two dimensions under time-delayed, non-linear feedback control. Specifically, the particle is subject to a force derived from…

In this note, we prove a version of the Phragmen-Lindelof principle using probabilistic techniques. In particular, we will show that if the p-th moment of the exit time of Brownian motion from a planar domain is finite, then an analytic…

We prove quantitative decay rates for the linearised Vlasov-Poisson system around compactly supported equilibria. More precisely, we prove decay of the gravitational potential induced by the radial dynamics of this system in the presence of…

The fractional Brownian motion can be considered as a Gaussian field indexed by $(t,H)\in {\mathbb{R}_{+}\times (0,1)}$, where $H$ is the Hurst parameter. On compact time intervals, it is known to be almost surely jointly H\"older…

In this paper, we consider transient subordinate Brownian motion X in R^d, d \geq 1, where the Laplace exponent \phi of the corresponding subordinator satisfies some mild conditions. The scaleinvariant Harnack inequality is proved for X. We…

The well known phenomenon of exponential contraction for solutions to the viscous Hamilton-Jacobi equation in the space-periodic setting is based on the Markov mechanism. However, the corresponding Lyapunov exponent $\lambda(\nu)$…