Related papers: Characterization Theorems for Generalized Function…
In this paper a general theory of semi-classical matrix orthogonal polynomials is developed. We define the semi-classical linear functionals by means of a distributional equation $D(u A) = u B,$ where $A$ and $B$ are matrix polynomials.…
In this paper, we study the asymptotic behavior of the normalized cadlag functions generated by the discrete Fourier transforms of a stationary centered square-integrable process, started at a point. We prove that the quenched invariance…
We define a class of random measures, spatially independent martingales, which we view as a natural generalisation of the canonical random discrete set, and which includes as special cases many variants of fractal percolation and Poissonian…
(Draft 3) A generalized differential operator on the real line is defined by means of a limiting process. These generalized derivatives include, as a special case, the classical derivative and current studies of fractional differential…
Analytical formulae for functional differentiation under simultaneous K-conservation constraints, with K the integral of some function of the functional variable, are derived, making the proper account for the simultaneous conservation of…
We study the Moyal evolution of the canonical position and momentum variables. We compare it with the classical evolution and show that, contrary to what is commonly found in the literature, the two dynamics do not coincide. We prove that…
We prove that the sequential functionals of some fixed types at type level 2, taking finite sequences of unary functions as arguments, do form a directed complete partial ordering. This gives a full characterisation of for which types the…
The causal perturbation expansion of the fermionic projector is performed with a contour integral method. Different normalization conditions are analyzed. It is shown that the corresponding light-cone expansions are causal in the sense that…
We study the Fock quantization of scalar fields of Klein-Gordon type in nonstationary scenarios propagating in spacetimes with compact spatial sections, allowing for different field descriptions that are related by means of certain nonlocal…
The central limit theorem of martingales is the fundamental tool for studying the convergence of stochastic processes, especially stochastic integrals and differential equations. In this paper, general central limit theorems and functional…
We calculate the large deviation functions characterizing the long-time fluctuations of the occupation of drifted Brownian motion and show that these functions have non-analytic points. This provides the first example of dynamical phase…
The main purpose of this article is to establish moderate deviation principles for additive functionals of bifurcating Markov chains. Bifurcating Markov chains are a class of processes which are indexed by a regular binary tree. They can be…
A general technique is developed for calculating functional determinants of second-order differential operators with Dirichlet, periodic, and antiperiodic boundary conditions. As an example, we give simple formulas for a harmonic oscillator…
A unification of characteristic mode decomposition for all method-of-moment formulations of field integral equations describing free-space scattering is derived. The work is based on an algebraic link between impedance and transition…
The functional Ito formula, firstly introduced by Bruno Dupire for continuous semimartingales, might be extended in two directions: different dynamics for the underlying process and/or weaker assumptions on the regularity of the functional.…
On the one side, the formalism of Global Transformations comes with the claim of capturing any transformation of space that is local, synchronous and deterministic. The claim has been proven for different classes of models such as mesh…
An explicit formula is obtained for the generalized Macdonald functions on the $N$-fold Fock tensor spaces, calculating a certain matrix element of a composition of several screened vertex operators. As an application, we prove the…
The compositional generalization abilities of neural models have been sought after for human-like linguistic competence. The popular method to evaluate such abilities is to assess the models' input-output behavior. However, that does not…
Many modern datasets, from areas such as neuroimaging and geostatistics, come in the form of a random sample of tensor-valued data which can be understood as noisy observations of a smooth multidimensional random function. Most of the…
We prove the existence of harmonic functions $f$ on trees, with respect to suitable transient transition operators $P$, that satisfy an analogue of Menshov universal property in the following sense: $f$ is the Poisson transform of a…