Related papers: Canonical spectral representation for exchangeable…
This work builds on an existing model of discrete canonical evolution and applies it to the general case of a linear dynamical system, i.e., a finite-dimensional system with configuration space isomorphic to $ \mathbb{R}^{q} $ and linear…
We show that extremal dynamics is very well modelled by the "Linear Fractional Stable Motion" (LFSM), a stochastic process entirely defined by two exponents that take into account spatio-temporal correlations in the distribution of active…
The extreme value dependence of regularly varying stationary time series can be described by the spectral tail process. Drees, Segers and Warchol [Extremes 18(3): 369--402, 2015] proposed estimators of the marginal distributions of this…
The problem of diagonalization of Hamiltonians of N-dimensional boson systems by means of time-dependent canonical transformations (CT) is considered, the case of quadratic Hamiltonians being treated in greater detail. The unitary generator…
In this paper we derive stochastic representations for the finite dimensional distributions of a multidimensional diffusion on a fixed time interval, conditioned on the terminal state. The conditioning can be with respect to a fixed point…
The problem of linear instability of a nonlinear traveling wave in a canonical Hamiltonian system with translational symmetry subject to superharmonic perturbations is discussed. It is shown that exchange of stability occurs when energy is…
The paper is dealing with semi-classical asymptotics of a characteristic function for a stochastic process. The main technical tool is provided by the stationary phase method. The extremal range for a stochastic process is defined by limit…
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…
We study the extremes for a class of a symmetric stable random fields with long range dependence. We prove functional extremal theorems both in the space of sup measures and in the space of cadlag functions of several variables. The limits…
This work identifies a solvable (in the sense that spectral correlation functions can be expressed in terms of orthogonal polynomials), rotationally invariant random matrix ensemble with a logarithmic weakly confining potential. The…
We review old and new uses of exchangeability, emphasizing the general theme of exchangeable representations of complex random structures. Illustrations of this theme include processes of stochastic coalescence and fragmentation; continuum…
The method of continuous canonical transformation is applied to the double exchange model with a purpose to eliminate the interaction term responsible for non conservation of magnon number. Set of differential equations for the effective…
Max-stable random fields can be constructed according to Schlather (2002) with a random function or a stationary process and a kind of random event magnitude. These are applied for the modelling of natural hazards. We simply extend these…
The aim of this paper is to provide models for spatial extremes in the case of stationarity. The spatial dependence at extreme levels of a stationary process is modeled using an extension of the theory of max-stable processes of de Haan and…
Canonical correlation analysis is a classical technique for exploring the relationship between two sets of variables. It has important applications in analyzing high dimensional datasets originated from genomics, imaging and other fields.…
A process-theoretic approach to electrodynamics based on persistent Kac-type stochastic processes is developed. Finite-velocity stochastic propagation is taken as primary, while relativistic wave equations arise as emergent descriptions…
We prove bounds on statistical distances between high-dimensional exchangeable mixture distributions (which we call \emph{permutation mixtures}) and their i.i.d. counterparts. Our results are based on a novel method for controlling $\chi^2$…
Discrete canonical evolution is a key tool for understanding the dynamics in discrete models of spacetime, in particular those represented by a triangular Regge lattice. We consider a finite-dimensional system whose evolution is realized by…
We consider non-ergodic class of stationary real harmonizable symmetric $\alpha$-stable processes $X=\left\{X(t):t\in\mathbb{R}\right\}$ with a finite symmetric and absolutely continuous control measure. We refer to its density function as…
Using the LePage representation, a strictly stable random element in a Banach space with $\alpha\in(0,2)$ can be represented as a sum of points of a Poisson process. This point process is union-stable, i.e. the union of its two independent…