Related papers: Non-symmetric stable processes: Dirichlet heat ker…
Let $(X,g)$ be a product cone with the metric $g=dr^2+r^2h$, where $X=C(Y)=(0,\infty)_r\times Y$ and the cross section $Y$ is a $(n-1)$-dimensional closed Riemannian manifold $(Y,h)$. We study the upper boundedness of heat kernel associated…
Consider the semiparametric transformation model $\Lambda_{\theta_o}(Y)=m(X)+\epsilon$, where $\theta_o$ is an unknown finite dimensional parameter, the functions $\Lambda_{\theta_o}$ and $m$ are smooth, $\epsilon$ is independent of $X$,…
The spinodal instabilities in hot asymmetric nuclear matter and some important critical parameters derived thereof are studied using six different families of relativistic mean-field (RMF) models. The slopes of the symmetry energy…
We establish sharp two-sided bounds on the heat kernel of the fractional Laplacian, perturbed by a drift having critical-order singularity, by transferring it to appropriate weighted space with singular weight.
In this article, we introduce an infinite-dimensional analogue of the $\alpha$-stable L\'evy motion, defined as a L\'evy process $Z=\{Z(t)\}_{t \geq 0}$ with values in the space $\mathbb{D}$ of c\`adl\`ag functions on $[0,1]$, equipped with…
We construct in the small-time setting the upper and lower estimates for the transition probability density of a L\'evy process in $\rn$. Our approach relies on the complex analysis technique and the asymptotic analysis of the inverse…
We consider a critical continuous-time branching process (a Yule process) in which the individuals independently execute symmetric $\alpha-$stable random motions on the real line starting at their birth points. Because the branching process…
We give an algorithm to construct a translation-invariant transport kernel between ergodic stationary random measures $\Phi$ and $\Psi$ on $\mathbb R^d$, given that they have equal intensities. As a result, this yields a construction of a…
We construct examples of translationally invariant solvable models of strongly-correlated metals, composed of lattices of Sachdev-Ye-Kitaev dots with identical local interactions. These models display crossovers as a function of temperature…
This article establishes a universal robust limit theorem under a sublinear expectation framework. Under moment and consistency conditions, we show that, for $\alpha \in(1,2)$, the i.i.d. sequence \[ \left \{ \left(…
We study from the numerical point of view, instabilities developed in a fluid layer with a free surface, in a cylindrical container which is non-homogeneously heated from below. In particular we consider the case in which the applied heat…
We consider the probability measures on Young diagrams in the $n \times k$ rectangle obtained by piecewise-continuously differentiable specializations of Schur polynomials in the dual Cauchy identity. We use a free fermionic representation…
We discuss an impact of various (path-wise) reflection-from-the barrier scenarios upon confining properties of a paradigmatic family of symmetric $\alpha $-stable L\'{e}vy processes, whose permanent residence in a finite interval on a line…
We consider a mixed boundary value problem in a domain $\Omega$ contained in a half-ball $B_+$ and having a portion $\bar{T}$ of its boundary in common with the curved part of $\partial B_+$. The problem has to do with some sort of…
We prove that the martingale problem is well posed for pure-jump L\'evy-type operators of the form $$ (\mathcal Lf)(x) = \int_{\mathbb R^d \setminus \{0\}} \left(f(x+h)-f(x) - (\nabla f(x) \cdot h)1_{\|h\| < 1}\right)K(x,h) dh, $$ where…
This article establishes explicit non-asymptotic ergodic bounds in the renormalized Wasserstein-Kantorovich-Rubinstein (WKR) distance for a viscous energy shell lattice model of turbulence with random energy injection. The system under…
On doubling metric measure spaces endowed with a strongly local regular Dirichlet form, we show some characterisations of pointwise upper bounds of the heat kernel in terms of global scale-invariant inequalities that correspond respectively…
We investigate the heat equation corresponding to the Bessel operators on a symmetric cone $\Omega=G/K$. These operators form a one-parameter family of elliptic self-adjoint second order differential operators and occur in the Lie algebra…
The problem of the Kosterlitz-Thouless (KT) transition in the highly frustrated XY Kagom\'{e} antiferromagnet is solved. The problem is mapped onto that of the KT transition in the XY ferromagnet on the hexagonal lattice. The transition…
We present an existence result for L\'evy-type processes which requires only weak regularity assumptions on the symbol $q(x,\xi)$ with respect to the space variable $x$. Applications range from existence and uniqueness results for…