Related papers: An Expansion for a Discrete Non-Lattice Distributi…
In nonlinear disordered Hamiltonian lattices, where there are no propagating phonons, the spreading of energy is of subdiffusive nature. Recently, the universality class of the subdiffusive spreading according to the nonlinear diffusion…
Linear statistics of random zero sets are integrals of smooth differential forms over the zero set and as such are smooth analogues of the volume of the random zero set inside a fixed domain. We derive an asymptotic expansion for the…
We introduce a novel technique to find the asymptotic time behaviour of deterministic systems exhibiting anomalous diffusion. The procedure is tested for various classes of simple but physically relevant 1-D maps and possible relevance of…
We extend two of the methods previously introduced to find discrete symmetries of differential equations to the case of difference and differential-difference equations. As an example of the application of the methods, we construct the…
In this paper we find asymptotic distribution for some unreliable networks. Using Markov Additive Structure and Adan, Foley, McDonald method, we find the exact asymptotic for the stationary distribution. With the help of MA structure and…
We study the propagation of non-classical light through arrays of coupled linear photonic waveguides and introduce some sets of refractive indices and coupling parameters that provide a closed form propagator in terms of orthogonal…
Consider a nearest-neighbor random walk with certain asymptotically zero drift on the positive half line. Let $M$ be the maximum of an excursion starting from $1$ and ending at $0.$ We study the distribution of $M$ and characterize its…
A semilinear singularly perturbed reaction-diffusion equation with Dirichlet boundary conditions is considered in a convex unbounded sector. The singular perturbation parameter is arbitrarily small, and the "reduced equation" may have…
We consider estimation procedures which are recursive in the sense that each successive estimator is obtained from the previous one by a simple adjustment. The model considered in the paper is very general as we do not impose any…
Products between phase-type distributed random variables and any independent, positive and continuous random variable are studied. Their asymptotic properties are established, and an expectation-maximization algorithm for their effective…
In this paper, we investigate the asymptotic error distributions of symplectic methods for stochastic Hamiltonian systems and further provide Hamiltonian-specific analysis that clarifies the superiority of symplectic methods. Our…
The higher-order Stokes phenomenon can emerge in the asymptotic analysis of many problems governed by singular perturbations. Indeed, over the last two decades, the phenomena has appeared in many physical applications, from acoustic and…
In this paper, an alternative Discrete skew Logistic distribution is proposed, which is derived by using the general approach of discretizing a continuous distribution while retaining its survival function. The properties of the…
In this paper, we prove asymptotic expansions of generalized partial theta functions with a nonprincipal Dirichlet character and relate these expansions to certain $L$-series.
We construct a point set in the Euclidean plane that elucidates the relationship between the fine-scale statistics of the fractional parts of $\sqrt n$ and directional statistics for a shifted lattice. We show that the randomly rotated, and…
We present several results that show somewhat surprising equidistribution patterns in the asymptotic behaviour of the argument of entire functions of finite order.
In some cases, solutions to nonlinear PDEs happen to be asymptotically (for large $x$ and/or $t$) invariant under a group $G$ which is not a symmetry of the equation. After recalling the geometrical meaning of symmetries of differential…
Dispersion relations are fundamental characteristics of the dynamics of quantum and wave systems. In this work we introduce a simple technique to generate arbitrary dispersion relations in a modulated tilted lattice. The technique is…
In 1962 Dyson used a physically based, macroscopic argument to deduce the first two terms of the large spacing asymptotic expansion of the gap probability for the bulk state of random matrix ensembles with symmetry parameter \beta. In the…
In this paper, we study the asymptotic behaviors of the extreme of mixed skew-t distribution. We considered limits on distribution and density of maximum of mixed skew-t distribution under linear and power normalization, and further derived…