Related papers: Nonlocal energy functionals and determinantal poin…
We study fractal properties of unbounded domains with infinite Lebesgue measure via their complex fractal dimensions. These complex dimensions are defined as poles of a suitable defined Lapidus fractal zeta function at infinity and are a…
We derive an integration by parts formula for functionals of determinantal processes on compact sets, completing the arguments of [4]. This is used to show the existence of a configuration-valued diffusion process which is non-colliding and…
For $\nu\in[0,1]$ and a complex parameter $\sigma,$ $Re\, \sigma>0,$ we discuss a linear inhomogeneous functional difference equation with variable coefficients on a complex plane $z\in\mathbb{C}$: \[…
We study the higher-order asymptotic development of a nonlocal phase transition energy in bounded domains and with prescribed external boundary conditions. The energy under consideration has fractional order $2s \in (0,1)$ and a first-order…
We consider the Wulff-type energy functional $$ \mathcal{W}_\Omega(u) := \int_\Omega B(H(\nabla u (x))) - F(u(x)) \, dx, $$ where $B$ is positive, monotone and convex, and $H$ is positive homogeneous of degree 1. The critical points of this…
Motivated by applications to the study of depth functions for tree-indexed random variables generated by point processes, we describe functional limit theorems for the intensity measure of point processes. Specifically, we establish uniform…
The integral fractional Laplacian of order $s \in (0,1)$ is a nonlocal operator. It is known that solutions to the Dirichlet problem involving such an operator exhibit an algebraic boundary singularity regardless of the domain regularity.…
We study the asymptotic convergence properties, as the time variable goes to infinity, of trajectories of second-order dissipative evolution equations combining potential with non-potential effects. We exhibit a sharp condition, involving…
Functional data present as functions or curves possessing a spatial or temporal component. These components by nature have a fixed observational domain. Consequently, any asymptotic investigation requires modelling the increased correlation…
We introduce a non-equilibrium density-functional theory of local temperature and associated local energy density that is suited for the study of thermoelectric phenomena. The theory rests on a local temperature field coupled to the…
We observe the Galton-Watson Branching Processes. Limit properties of transition functions and their convergence to invariant measures are investigated.
In this paper, using the theory developed in [8], we obtain some results of a totally new type about a class of non-local problems. Here is a sample: Let $\Omega\subset {\bf R}^n$ be a smooth bounded domain, with $n\geq 4$, let $a, b,…
We study the well-posedness of a class of nonlocal-interaction equations on general domains $\Omega\subset \mathbb{R}^d$, including nonconvex ones. We show that under mild assumptions on the regularity of domains (uniform prox-regularity),…
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…
We consider a nonlinear parabolic equation with an exponential nonlinearity which is critical with respect to the growth of the nonlinearity and the regularity of the initial data. After showing the equivalence of the notions of weak and…
When a parameter of interest is nondifferentiable in the probability, the existing theory of semiparametric efficient estimation is not applicable, as it does not have an influence function. Song (2014) recently developed a local asymptotic…
The paper deals with second order parabolic equations on bounded domains with Dirichlet conditions in arbitrary Euclidean spaces. Their interest comes from being models for describing reaction-diffusion processes in several frameworks. A…
We study the local behavior of the elements of a specific energy class of functions, called the nonlocal parabolic ($p$-homogenous) De Giorgi class. First we carry on an analysis of their local boundedness under optimal tail conditions, and…
In this paper we study the asymptotic behaviour of a nonlocal nonlinear parabolic equation governed by a parameter. After giving the existence of unique branch of solutions composed by stable solutions in stationary case, we gives for the…
We study the asymptotic behavior of a family of functionals which penalize a short-range interaction of convolution type between a finite perimeter set and its complement. We first compute the pointwise limit and we obtain a lower estimate…