相关论文: The Characteristic Function of the Cube of a Gauss…
The relation between continuous functions and random vectors is revealed in the paper that the main meaning is described as, for any given continuous function, there must be a sequence of probability spaces and a sequence of random vectors…
This paper considers the problem of estimating the cumulative distribution function and probability density function of a random variable using data quantized by uniform and non-uniform quantizers. A simple estimator is proposed based on…
In this paper we give a method, based on the characteristic function of a set, to solve some difficult problems of set theory in undergraduate research.
We show that, in a restricted range, the divisor function of integers in residue classes modulo a prime follows a Gaussian distribution, and a similar result for Hecke eigenvalues of classical holomorphic cusp forms. Furthermore, we obtain…
We compute analytically, for large N, the probability distribution of the number of positive eigenvalues (the index N_{+}) of a random NxN matrix belonging to Gaussian orthogonal (\beta=1), unitary (\beta=2) or symplectic (\beta=4)…
We investigate the characteristic polynomials of the Gaussian $\beta$-ensemble for general $\beta>0$ through its transfer matrix recurrence. We show that the rescaled characteristic polynomial converges to a random entire function in a…
A quantum probability measure is a function on a sigma-algebra of subsets of a (locally compact and Hausdorff) sample space that satisfies the formal requirements for a measure, but whose values are positive operators acting on a complex…
The paper addresses the question whether a random functional, a map from a set $E$ into the space of real-valued measurable functions on a probability space, has a measurable version with values in ${\mathbb R}^E$. Similarly, one may ask…
In probability theory, the partition function is a factor used to reduce any probability function to a density function with total probability of one. Among other statistical models used to represent joint distribution, Markov random fields…
Stochastic realization of the wave function in quantum mechanics, with the inclusion of soliton representation of extended particles, is discussed. The concept of Stochastic Qubits is used for quantum computing modeling.
Linear combinations of chi square random variables occur in a wide range of fields. Unfortunately, a closed, analytic expression for the pdf is not yet known. As a first result of this work, an explicit analytic expression for the density…
We present bounds of quadratic form for the logarithm of the Gaussian Q-function. We also show an analytical method for deriving log-quadratic approximations of the Q-function and give an approximation with absolute error less than…
We determine the expected curvature polynomial of random real projective varieties given as the zero set of independent random polynomials with Gaussian distribution, whose distribution is invariant under the action of the orthogonal group.…
In this paper, we study the tensor product of two unitary irreducible representations, as well as the tensor product of a unitary irreducible representation with a finite-dimensional one, and determine the corresponding Clebsch-Gordan…
We study some properties of hyperbolic Gaussian analytic functions of intensity $L$ in the unit ball of $\mathbb C^n$. First we deal with the asymptotics of fluctuations of linear statistics as $L\to\infty$. Then we estimate the probability…
The full spectrum of transfer matrices of the general eight-vertex model on a square lattice is obtained by numerical diagonalization. The eigenvalue spacing distribution and the spectral rigidity are analyzed. In non-integrable regimes we…
We characterize the generating function of the number of representations described in the title in terms of the theory of modular forms. Appealing to this characterization we obtain explicit formulas for the representation numbers as…
The quantum propagator and characteristic equation in the presence of a chain of $\delta$-potentials are obtained in the rectangular, cylindrical and spherical coordinate systems. The simplicity and efficiency of the method is illustrated…
We introduce the characteristic numbers and the chromatic polynomial of a tensor. Our approach generalizes and unifies the chromatic polynomial of a graph and of a matroid, characteristic numbers of quadrics in Schubert calculus, Betti…
A combinatorial formula to generate U(N) character expansions is presented. It is shown that the resulting character expansion formulas greatly simplify a number of problems where integrals over the group manifolds need to be calculated.…