Related papers: Limit theorems for a stable sausage
In this article, we introduce Brownian motion on stable looptrees using resistance techniques. We prove an invariance principle characterising it as the scaling limit of random walks on discrete looptrees, and prove precise local and global…
We propose a mechanism to produce fluctuations in the viscosity parameter ($\alpha$) in differetially rotating discs. We carried out a nonlinear analysis of a general accretion flow, where any perturbation on the background $\alpha$ was…
We summarize recent results on the volume dependence of the location of the critical endpoint in the QCD phase diagram. To this end, we employ a sophisticated combination of Lattice Yang--Mills theory and a (truncated) version of…
Functional limit theorems are presented for the rescaled occupation time fluctuations process of a critical finite variance branching particle system in $R^d$ with symmetric a-stable motion starting off from either a standard Poisson random…
The paper deals with the problem of stability for the flow of the 1D Burgers equation on a circle. Using some ideas from the theory of positivity preserving semigroups, we establish the strong contraction in the $L^1$ norm. As a…
We investigate the long-range statistical correlations, whereby discuss the nature of the undermining interacting/ noninteracting domains and associated phase transitions under variations of the quark mass and the mass scale that…
We discuss the fluctuation properties of equilibrium chaotic systems with constraints such as iso-kinetic and Nos\'e-Hoover thermostats. Although the dynamics of these systems does not typically preserve phase-space volumes, the average…
We consider a locally regulated spatial population model introduced by Bolker and Pacala. Based on the deterministic approximation studied by Fournier and M\'el\'eard, we prove that the fluctuation theorem holds under some mild moment…
We numerically analyse the rotation of a neutrally buoyant spheroid in a shear flow at small shear Reynolds number. Using direct numerical stability analysis of the coupled nonlinear particle-flow problem we compute the linear stability of…
We establish sharp regularity estimates for solutions to $Lu=f$ in $\Omega\subset\mathbb R^n$, being $L$ the generator of any stable and symmetric L\'evy process. Such nonlocal operators $L$ depend on a finite measure on $S^{n-1}$, called…
The sunflower equation describes the motion of the tip of a plant due to the auxin transportation under the influence of gravity. This work proposes the fractional-order generalization to this delay differential equation. The equation…
We consider internal diffusion limited aggregation in dimension larger than or equal to two. This is a random cluster growth model, where random walks start at the origin of the d-dimensional lattice, one at a time, and stop moving when…
We study Brownian loop soup clusters in $\mathbb{R}^3$ for an arbitrary intensity $\alpha>0$. We show the existence of a phase transition for the presence of unbounded clusters and study its basic properties. In particular, we show that,…
A functional limit theorem is established for the partial-sum process of a class of stationary sequences which exhibit both heavy tails and long-range dependence. The stationary sequence is constructed using multiple stochastic integrals…
We prove that for q>=1, there exists r(q)<1 such that for p>r(q), the number of points in large boxes which belongs to the infinite cluster has a normal central limit behaviour under the random cluster measure phi_{p,q} on Z^d, d>=2.…
Let $(Z_t)_{t\geq 0}$ denote the derivative martingale of branching Brownian motion, i.e.\@ the derivative with respect to the inverse temperature of the normalized partition function at critical temperature. A well-known result by Lalley…
We derive a simple closed analytical expression for the total entropy production along a single stochastic trajectory of a Brownian particle diffusing on a periodic potential under an external constant force. By numerical simulations we…
We study the stability of quantum motion of classically regular systems in presence of small perturbations. Onthe base of a uniform semiclassical theory we derive the fidelity decay which displays a quite complexbehaviour, from Gaussian to…
In this paper we establish rigorously that the family of Burgers vortices of the three-dimensional Navier-Stokes equation is stable for small Reynolds numbers. More precisely, we prove that any solution whose initial condition is a small…
In this note we study the error term R_{n,L}(x) in the generalized circle problem for a ball of volume x and a random lattice L of large dimension n. Our main result is the following functional central limit theorem: Fix an arbitrary…