相关论文: Trace Estimates for Stable Processes
In this paper we consider the persistence properties of random processes in Brownian scenery, which are examples of non-Markovian and non-Gaussian processes. More precisely we study the asymptotic behaviour for large $T$, of the probability…
We address a conjecture of D. Applebaum on small time trace asymptotics for subordinate Brownian motion on compact manifolds.
Extensive numerical evidence shows that the assimilation of observations has a stabilizing effect on unstable dynamics, in numerical weather prediction and elsewhere. In this paper, we apply mathematically rigorous methods to showing why…
In this paper, we rely on the additive decomposition in law satisfied by a class of stochastic processes, combined with the well-known regulariy properties of fractional Brownian motion, to establish Besov-Orlicz regularity of their sample…
Martin boundaries and integral representations of positive functions which are harmonic in a bounded domain $D$ with respect to Brownian motion are well understood. Unlike the Brownian case, there are two different kinds of harmonicity with…
We consider a quantum system of non-interacting fermions at temperature T, in the framework of linear response theory. We show that semiclassical theory is an appropriate framework to describe some of their thermodynamic properties, in…
We prove that the ground state eigenfunction for symmetric stable processes of order $\alpha\in (0, 2)$ killed upon leaving the interval $(-1, 1)$ is concave on $(-{1/2}, {1/2})$. We call this property "mid--concavity." A similar statement…
System of partial differential equations with a convolution terms and non-local nonlinearity describing oscillations of plate due to Berger approach and with accounting for thermal regime in terms of Coleman-Gurtin and Gurtin-Pipkin law and…
We study the geometry of a semiflexible polymer at finite temperatures. The writhe can be calculated from the properties of Gaussian random walks on the sphere. We calculate static and dynamic writhe correlation functions. The writhe of a…
This paper studies the asymptotic behavior of a one-dimensional Type II porous thermoelastic system with a conservative porous structure and local memory damping applied to the elastic component. Using frequency domain resolvent estimates,…
We propose an embedding of standard active particle models in terms of two-temperature processes. One temperature refers to an ambient thermal bath, and the other temperature effectively describes ``hot spots,'' i.e., systems with few…
We show in the smooth category that the heat trace asymptotics and the heat content asymptotics can be made to grow arbitrarily rapidly. In the real analytic context, however, this is not true and we establish universal bounds on their…
In most interacting many-body systems associated with some "emergent phenomena," we can identify sub-groups of degrees of freedom that relax on dramatically different time-scales. Time-scale separation of this kind is particularly helpful…
The statistical physics of homogeneous DNA is investigated by the imaginary time path integral formalism. The base pair stretchings are described by an ensemble of paths selected through a macroscopic constraint, the fulfillement of the…
Using a thermodynamically consistent, mesoscopic model for modern complementary metal-oxide-semiconductor transistors, we study an array of logical circuits and explore how their function is constrained by recent thermodynamic uncertainty…
We derive the asymptotic behavior of hitting probability at small target of size $O(\epsilon)$ for reflected Brownian motion in domains with suitable smooth boundary conditions, where the boundary of domain contains both reflecting part,…
In two recent papers [5] and [6], we generalized some classical results of Harmonic Analysis using probabilistic approach by means of a d- dimensional rotationally symmetric stable process. These results allow one to discuss some…
We consider the solid or hexatic non-equilibrium phases of an interacting two-dimensional system of Active Brownian Particles at high density and investigate numerically and theoretically the properties of the velocity distribution function…
We address the dynamical and statistical description of stably stratified turbulent boundary layers with the important example of the atmospheric boundary layer with a stable temperature stratification in mind. Traditional approaches to…
The spectral heat content of a domain $\Omega\subset\mathbb{R}^d$ corresponding to a $d$-dimensional stochastic process $X=(X_t)_{t\ge 0}$ is defined as \[Q^{X}_\Omega(t)=\int_{\mathbb{R}^d} \mathbb{P}_x(\tau^X_\Omega>t)dx,\] where…