Related papers: Bessel bridge representation for heat kernel in hy…
For Poisson particle processes in hyperbolic space we introduce and study concepts analogous to the intersection density and the mean visible volume, which were originally considered in the analysis of Boolean models in Euclidean space. In…
We represent the free energy functional by a diagrammatic series with tensorial coefficients indexed by powers of length scale. For hard cores, we obtain Percus' exact functional in one dimension and the Kierlik-Rosinberg form of…
Understanding how molecular correlations give rise to mesoscale organization is central to the physics of complex fluids such as hydrogen-bonded mixtures. In this work, we develop a mesoscale bridge formalism that connects the site-site…
For some discrete parameters $k\ge0$, multivariate (Dunkl-)Bessel processes on Weyl chambers $C$ associated with root systems appear as projections of Brownian motions without drift on Euclidean spaces $V$, and the associated transition…
Recent conjectures on the complexity of black holes suggest that their evolution manifests in the structural properties of Einstein-Rosen bridges, like the length and volume. The complexity of black holes relates to the computational…
The purpose of this paper is to characterize the homogeneous Besov space in the Dunkl setting. We utilize a new discrete reproducing formula, that is, the building blocks are differences of the Dunkl-Poisson kernel which involves both the…
Phonon heat transport in mesoscopic systems is investigated using methods analogous to the Landauer description of electrical conductance. A "universal heat conductance" expression that depends on the properties of the conducting pathway…
Compressibility transformations are used to relate hypersonic zero-pressure-gradient (ZPG) turbulent boundary layers (TBLs) to incompressible reference states, but their assessment has largely focused on the collapse of transformed mean…
In this article we demonstrate that dynamical quantum phase transitions occur for an exemplary higher order topological insulator, the Benalcazar-Bernevig-Hughes model, following quenches across a topological phase boundary. A dynamical…
The interacting quantum Bose gas is a random ensemble of many Brownian bridges (cycles) of various lengths with interactions between any pair of legs of the cycles. It is one of the standard mathematical models in which a proof for the…
In light of the inherent entailment relations between images and text, hyperbolic point vector embeddings, leveraging the hierarchical modeling advantages of hyperbolic space, have been utilized for visual semantic representation learning.…
In this article, we use the second intrinsic volume to define a metric on the space of homothetic classes of Gaussian bounded convex bodies in a separable real Hilbert space. Using kernels of hyperbolic type, we can deduce that this space…
We obtain the uniform convergence rate for the Gaussian fluctuation of the radial part of the Brownian motion on a hyperbolic space. We also show that this result is sharp if the dimension of the hyperbolic space is two or general odd. Our…
The need to understand the structure of hierarchical or high-dimensional data is present in a variety of fields. Hyperbolic spaces have proven to be an important tool for embedding computations and analysis tasks as their non-linear nature…
Bessel process is defined as the radial part of the Brownian motion (BM) in the $D$-dimensional space, and is considered as a one-parameter family of one-dimensional diffusion processes indexed by $D$, BES$^{(D)}$. It is well-known that…
Understanding the generation mechanism of the heating flux is essential for the design of hypersonic vehicles. We proposed a novel formula to decompose the heat flux coefficient into the contributions of different terms by integrating the…
Many inverse problems require reconstructing physical fields from limited and noisy data while incorporating known governing equations. A growing body of work within probabilistic numerics formalizes such tasks via Bayesian inference in…
The heat kernel or Bargmann-Segal transform on a noncompact Riemannian symmetric space X=G/K maps a square integrable function on X to a holomorphic function on the complex crown. In this article we determine the range of this transform.
The aim of this paper is threefold. First, we obtain the precise bounds for the heat kernel on isotropic Heisenberg groups by using well-known results in the three dimensional case. Second, we study the asymptotic estimates at infinity for…
The one-loop effects to the Dirac action of $p$-branes in a hyperbolic background from the path integral and the solution of the Wheeler-DeWitt equation are analysed. The objective of comparing the equivalent quantization procedures is to…