Related papers: Remarks on restricted Nevanlinna transforms
In a recent letter ({\it{EPL}}, {\bf{104}} (2013) 60003; see also {\it {arXiv:1309.5645}}), Plastino and Rocca suggest that the divergences inherent to the formulation of nonextensive statistical mechanics can be eliminated {\it {via}} the…
A canonical formalism and constraint analysis for discrete systems subject to a variational action principle are devised. The formalism is equivalent to the covariant formulation, encompasses global and local discrete time evolution moves…
The Weyl-Wigner-Moyal formalism for Dirac second class constrained systems has been proposed recently as the deformation quantization of Dirac bracket. In this paper, after a brief review of this formalism, it is applied to the case of the…
A complex function $f(z)$ is called a Herglotz-Nevanlinna function if it is holomorphic in the upper half-plane ${\mathbb C}_+$ and maps ${\mathbb C}_+$ into itself. By a maximum principle a Herglotz-Nevanlinna function which takes a real…
We present a simplified explanation of why free fractional convolution corresponds to the differentiation of polynomials, by finding how the finite free cumulants of a polynomial behave under differentiation. This approach allows us to…
We introduce a new notion of influence for symmetric convex sets over Gaussian space, which we term "convex influence". We show that this new notion of influence shares many of the familiar properties of influences of variables for monotone…
The approach to the theory of a relativistic random process is considered by the path integral method as Brownian motion taking into account the boundedness of speed. An attempt was made to build a relativistic analogue of the Wiener…
Since Voiculescu introduced his bi-free probability theory in 2013, the major development of the theory has been on its combinatorial side; in particular, on the combinatorics of bi-free cumulants and its application to the bi-free…
This article describes the various experimental bounds on the variation of the fundamental constants of nature. After a discussion on the role of fundamental constants, of their definition and link with metrology, the various constraints on…
Constrained symplectic quantization is a functional formulation of quantum field theory in which quantum fluctuations are sampled through a deterministic Hamiltonian flow in an auxiliary intrinsic time $\tau$. In this paper we extend the…
Let $\Omega$ be a Cartan domain and $K = \sum_{\underline s}a_{\underline s}K_{\underline s}$ be a $\mathbb K$-invariant kernel on $\Omega$. In this article, we first obtain a necessary condition on $K$ to have the complete Nevanlinna-Pick…
Nevanlinna showed that Cauchy transforms of probability measures parametrize all functions from the upper half plane into itself satisfying a certain asymptotic condition at infinity. We show that the correspondence fails in general for the…
An estimation method is proposed for a wide variety of discrete time stochastic processes that have an intractable likelihood function but are otherwise conveniently specified by an integral transform such as the characteristic function,…
A simple example of an $n$-dimensional admissible complex of planes is given for the overdetermined $k$-plane transform in $\mathbb{R}^n$. For the corresponding restricted $k$-plane transform sharp existence conditions are obtained and…
The Thirring model with random couplings is a translationally invariant generalisation of the SYK model to 1+1 dimensions, which is tractable in the large N limit. We compute its two point function, at large distances, for any strength of…
Let $K$ be a number field, and let $K(x_1,...,x_d)$ be the field of rational fractions in the variables $x_1,...,x_d$. In this paper, we introduce two kinds of Laplace transform adapted to solutions of the differential…
Neural network representations are often analyzed as vectors in a fixed Euclidean space. However, their coordinates are not uniquely defined. If a hidden representation is transformed by an invertible linear map, the network function can be…
Recent theoretical ideas and observational claims suggest that the fine structure constant alpha may be variable. We examine a spectrum of models in which alpha is a function of a scalar field. Specifically, we consider three scenarios:…
We introduce a class of probability measures whose densities near infinity are mixtures of Pareto distributions. This class can be characterized by the Fourier transform which has a power series expansion including real powers, not only…
Unlike classical and free independence, the boolean and monotone notions of independence lack of the property of independent constants. In the scalar case, this leads to restrictions for the central limit theorems, as observed by F.…