Related papers: HCM Property and the Half-Cauchy Distribution

Measurements of a weighted energy density average taken in the vacuum state of a conformal field theory in $1+1$ dimensions are randomly distributed with vanishing expectation value. The probability distribution is computed in closed form…

We consider the statistical properties of the gravitational field F in an infinite one-dimensional homogeneous Poisson distribution of particles, using an exponential cut-off of the pair interaction to control and study the divergences…

We study the quantum localization in the chaotic eigenstates of a billiard with mixed-type phase space, after separating the regular and chaotic eigenstates, in the regime of slightly distorted circle billiard where the classical transport…

We examine the distributions of non-commutative polynomials of non-atomic, freely independent random variables. In particular, we obtain an analogue of the Strong Atiyah Conjecture for free groups thus proving that the measure of each atom…

When a Hamiltonian density is bounded by below, we know that the lowest-energy state must be stable. One is often tempted to reverse the theorem and therefore believe that an unbounded Hamiltonian density always implies an instability. The…

We consider the Cauchy problem for one-dimensional dispersive equations with a general nonlinearity in the periodic setting. Our main hypotheses are both that the dispersive operator behaves for high frequencies as a Fourier multiplier by $…

Consider a semiclassical Hamiltonian $H := h^{2} \Delta + V - E$ where $\Delta$ is the positive Laplacian on $\mathbb{R}^{d}$, $V \in C^{\infty}_{0}(\mathbb{R}^{d})$ and $E > 0$ is an energy level. We prove that under an appropriate…

The problem of calculating the probability density and distribution function of a strictly stable law is considered at $x\to0$. The expansions of these values into power series were obtained to solve this problem. It was shown that in the…

Let $\{x_{\alpha}\}_{\alpha \in \mathbb{Z}}$ and $\{y_{\alpha}\}_{\alpha \in \mathbb{Z}}$ be two independent collections of zero mean, unit variance random variables with uniformly bounded moments of all orders. Consider a nonsymmetric…

A numerical experiment of ideal stochastic motion of a particle subject to conservative forces and Gaussian noise reveals that the path probability depends exponentially on action. This distribution implies a fundamental principle…

Let ${\bf L}$ be the unit exponential random variable and ${\bf Z}_\alpha$ the standard positive $\alpha$-stable random variable. We prove that $\{(1-\alpha) \alpha^{\gamma_\alpha} {\bf Z}_\alpha^{-\gamma_\alpha}, 0< \alpha <1\}$ is…

We establish a comprehensive probability theory for coherent transport of random waves through arbitrary linear media. The transmissivity distribution for random coherent waves is a fundamental B-spline with knots at the transmission…

The stability of random variables can be generalized in any convex cone. In this case the principal results about the LePage representation and the domains of attraction are analogous but different to those well known for general Banach…

Let $X_N$ be an $N\ts N$ random symmetric matrix with independent equidistributed entries. If the law $P$ of the entries has a finite second moment, it was shown by Wigner \cite{wigner} that the empirical distribution of the eigenvalues of…

A random variable X is strictly stable if a sum of independent copies of X has the same distribution as X up to scaling, and is stable (in the broad sense) if the sum has the same distribution as X up to both scaling and shifting. Steutel…

Let $X=(X_t)$ be a one-dimensional Ornstein-Uhlenbeck process with an initial density function $f$ supported on the positive real-line that is a regularly varying function with exponent $-(1+\eta)$, with $\eta\in (0,1)$. We prove the…

It is shown that the energy of a mode of a classical chaotic field, following the continuous exponential distribution as a classical random variable, can be uniquely decomposed into a sum of its fractional part and of its integer part. The…

We analyze the time-dependent free energy functionals of the semiclassical one-dimensional Bose-Hubbard chain. We first review the weakly chaotic dynamics and the consequent early-time anomalous diffusion in the system. The anomalous…

We investigate the analytical properties of the $\alpha-$Sun random variable, which arises from the domain of attraction of certain storage models involving a maximum and a sum. In the Fr\'echet case we show that this random variable is…

We perform a detailed numerical study of the conductance $G$ through one-dimensional (1D) tight-binding wires with on-site disorder. The random configurations of the on-site energies $\epsilon$ of the tight-binding Hamiltonian are…