Related papers: The compact support property for the $\Lambda$-Fle…
In this paper, we establish limit theorems for the supremum of the support, denoted by $M_t$, of a supercritical super-Brownian motion $\{X_t, t\ge0\}$ on $\mathbb{R}$. We prove that there exists an $m(t)$ such that $(X_t-m(t), M_t-m(t))$…
We study the density of the support of a dyadic $d$-dimensional branching Brownian motion (BBM) in subcritical balls in $\mathbb{R}^d$. Using elementary geometric arguments and an extension of a previous result on the probability of absence…
This article contains both a point process and a sequential description of the greatest convex minorant of Brownian motion on a finite interval. We use these descriptions to provide new analysis of various features of the convex minorant…
By considering a counting-type argument on Brownian sample paths, we prove a result similar to that of Orey and Taylor on the exact Hausdorff dimension of the rapid points of Brownian motion. Because of the nature of the proof we can then…
The dynamical effect of the cosmological constant $\Lambda$ on a single spherical void evolving in a the universe is investigated within a non linear perturbation of Newton-Friedmann models. The void expands with a huge initial burst which…
It has been conjectured since the work of Lalley and Sellke (1987) that the branching Brownian motion seen from its tip (e.g. from its rightmost particle) converges to an invariant point process. Very recently, it emerged that this can be…
We study condensation in several particle systems related to the inclusion process. For an asymmetric one-dimensional version with closed boundary conditions and drift to the right, we show that all but a finite number of particles condense…
We prove the cut-off phenomenon in total variation distance for the Brownian motions traced on the classical symmetric spaces of compact type, that is to say: (1) the classical simple compact Lie groups: special orthogonal groups, special…
We identify a class of continuous compactly supported functions for which the known part of the Gabor frame set can be extended. At least for functions with support on an interval of length two, the curve determining the set touches the…
We consider the median of n independent Brownian motions, and show that this process, when properly scaled, converges weakly to a centered Gaussian process. The chief difficulty is establishing tightness, which is proved through direct…
To address the dynamics of a Brownian particle on a periodic symmetric substrate under high-frequency periodic forcing with a vanishing time average, we construct an effective Langevin dynamics by invoking Kapitza-Landau time window. Our…
We derive a new theoretical lower bound for the expected supremum of drifted fractional Brownian motion with Hurst index $H\in(0,1)$ over (in)finite time horizon. Extensive simulation experiments indicate that our lower bound outperforms…
We raise a question on whether a dynamical system driven by Markov process is Markovian, for which we are able to propose a criterion and examples of positive case. This investigation leads us to develop (i) a general construction of…
We prove the existence of a compact random attractor for the stochastic Benjamin-Bona-Mahony Equation defined on an unbounded domain. This random attractor is invariant and attracts every pulled-back tempered random set under the forward…
Modulated accelerating mirrors provide a concrete dynamical origin for the $\kappa\gamma$ vacuum-a thermal, single-mode squeezed state with a tunable angle. The Carlitz-Willey trajectory fixes the Planckian weights (set by $\kappa$), while…
We consider the coadjoint action of a Loop group of a compact group on the dual of the corresponding centrally extended Loop algebra and prove that a Brownian motion in a Cartan subalgebra conditioned to remain in an affine Weyl chamber -…
We consider the physically relevant fully compressible setting of the Rayleigh Benard problem of a fluid confined between two parallel plates, heated from the bottom, and subjected to the gravitational force. Under suitable restrictions…
This article establishes cutoff convergence or abrupt convergence of three statistical quantities for multivariate (Hurwitz) stable geometric Brownian motion: the autocorrelation function, the Wasserstein distance between the current state…
In this paper we prove the existence of a large class of periodic solutions of the Vlasov-Poisson in one space dimension that decay exponentially as t goes to infinity. The exponential decay is well known for the linearized version of the…
We solve the problem of formulating Brownian motion in a relativistically covariant framework in 1+1 and 3+1 dimensions. We obtain covariant Fokker-Planck equations with (for the isotropic case) a differential operator of invariant…