Related papers: Intertwining and Duality for Consistent Markov Pro…
Markovian intertwining relations between two Markov semigroups are related to the partial inclusion of the spectra of their generators, at least for finite ergodic processes. We check the limitations of this observation by investigating the…
It is long known that quantum Calogero models feature intertwining operators, which increase or decrease the coupling constant by an integer amount, for any fixed number of particles. We name these as ``horizontal'' and construct new…
The strict relation between some class of multiboson hamiltonian systems and the corresponding class of orthogonal polynomials is established. The correspondence is used effectively to integrate the systems. As an explicit example we…
We consider the statistical mechanics of a system of topologically linked polymers, such as for instance a dense solution of polymer rings. If the possible topological states of the system are distinguished using the Gauss linking number as…
A new derivation method of duality relations in stochastic processes is proposed. The current focus is on the duality between stochastic differential equations and birth-death processes. Although previous derivation methods have been based…
Interacting particle systems can often be constructed from a graphical representation, by applying local maps at the times of associated Poisson processes. This leads to a natural coupling of systems started in different initial states. We…
We consider the exactly solvable quantum mechanical systems whose eigenfunctions are described by the multi-indexed orthogonal polynomials of Laguerre, Jacobi, Wilson and Askey-Wilson types. Corresponding to the recurrence relations with…
Duality in the integrable systems arising in the context of Seiberg-Witten theory shows that their tau-functions indeed can be seen as generating functions for the mutually Poisson-commuting hamiltonians of the {\em dual} systems. We…
We study general properties for the family of stochastic processes with polynomial regression property, that is that every conditional moment of the process is a polynomial. It turns out that then there exists a family of polynomial…
We study the correlations (and alignment as a particular case) existent between the fragments originated in a decaying process when the daughter particles interact. The interaction between the particles is modeled using the potential of…
We define the set of almost-intertwining matrices to be all triples(X,Y,Z) of n x n matrices for which XZ=YX+T for some rank one matrix T. A surprisingly simple formula is given for tau-functions of the KP hierarchy in terms of such…
In this article we apply a discrete action principle for the Vlasov--Maxwell equations in a structure-preserving particle-field discretization framework. In this framework the finite-dimensional electromagnetic potentials and fields are…
This paper reviews a class of univariate piecewise polynomial functions known as discrete splines, which share properties analogous to the better-known class of spline functions, but where continuity in derivatives is replaced by (a…
We construct new families of discrete vector orthogonal polynomials that have the property to be eigenfunctions of some difference operator. They are extensions of Charlier, Meixner and Kravchuk polynomial systems. The ideas behind our…
In this paper we use duality techniques to study a combination of the well-known contact process (CP) and the somewhat less-known annihilating branching process. As the latter can be seen as a cancellative version of the contact process, we…
Self-assembly in natural and synthetic molecular systems can create complex aggregates or materials whose properties and functionality rises from their internal structure and molecular arrangement. The key microscopic features that control…
This survey article gives an elementary introduction to the algebraic approach to Markov process duality, as opposed to the pathwise approach. In the algebraic approach, a Markov generator is written as the sum of products of simpler…
Technical systems have evolved over time into large and complex Interwoven Systems consisting of several to a huge number of (possibly heterogeneous) subsystems that have interdependencies. The resultant mutual influences among subsystems…
We study properties of a subclass of Markov processes that have all moments that are continuous functions of the time parameter and more importantly are characterized by the property that say their $n-$th conditional moment given the past…
Recent times have seen a spurt of research activity focused on "completing" certain wave-particle duality relations using entanglement or polarization. These studies use a duality relation involving path-predictability, and not…