Related papers: $q$-Deformed Discrete Whittaker Processes
A general affine Markov semigroup is formulated as the convolution of a homogeneous one with a skew convolution semigroup. We provide some sufficient conditions for the regularities of the homogeneous affine semigroup and the skew…
Non--minimal $q$-deformations are defined. Their role in the explicit construction of the matrix elements of the generators of ${\cal U}_{q}(SO(5))$ on suitably parametrized bases are exhibited. The implications are discussed.
It has been shown by Hacking and Prokhorov that if the projective surface X with quotient singularities and self-intersection number 9 has a smoothing to the projective plane, then X is the general fiber of a Q-Gorenstein deformation of the…
We construct a class of discontinuous superprocesses with dependent spatial motion and general branching mechanism. The process arises as the weak limit of critical interacting-branching particle systems where the spatial motions of the…
The aim of this article is to prove that diffusion processes in $\mathbb{R}^d$ with a drift can be approximated by suitable Markov chains on $n^{-1}\mathbb{Z}^d$. Moreover, we investigate sufficient conditions on the conductances which…
We numerically study Barrett-Crane models of Riemannian quantum gravity. We have extended the existing numerical techniques to handle q-deformed models and arbitrary space-time triangulations. We present and interpret expectation values of…
We consider quantum supergroups that arise in non-anticommutative deformations of N=(1/2,1/2) and N=(1,1) four-dimensional Euclidean supersymmetric theories. Twist operators in the corresponding deformed algebras of superfields contain left…
We consider q-deformations of Witt rings, based on geometric operations on zeta functions of motives over finite fields, and we use these deformations to construct q-analogs of the Bost-Connes quantum statistical mechanical system. We show…
We study deformations of two-component non semisimple Poisson pencils of hydrodynamic type associated with Balinski\v{\i}-Novikov algebras. We show that in most cases the second order deformations are parametrized by two functions of a…
The stochastic theory of non-relativistic quantum mechanics presented here relies heavily upon the theory of stochastic processes, with its definitions, theorems and specific vocabulary as well. Its main hypothesis states indeed that the…
The two-dimensional Radon transform of the Wigner quasiprobability is introduced in canonical form and the functions playing a role in its inversion are discussed. The transformation properties of this Radon transform with respect to…
In this work, we present straightforward and concrete computations of the unitary irreducible representations of the Euclidean motion group $M(2)$ employing the methods of deformation quantization. Deformation quantization is a quantization…
This paper deals with quon algebras or deformed oscillator algebras, for which the deformation parameter is a root of unity. We show the interest of such algebras for fractional supersymmetric quantum mechanics, angular momentum theory and…
A Markov assumption considers a physical system memoryless to simplify its dynamics. Whereas memory effect or the non-Markovian phenomenon is more general in nature. In the quantum regime, it is challenging to define or quantify the…
Markov process is widely applied in almost all aspects of literature, especially important for understanding non-equilibrium processes. We introduce a decomposition to general Markov process in this paper. This decomposition decomposes the…
Piecewise-deterministic Markov processes form a general class of non-diffusion stochastic models that involve both deterministic trajectories and random jumps at random times. In this paper, we state a new characterization of the jump rate…
A new and rather broad class of stationary (i.e. stochastically translation invariant) random tessellations of the $d$-dimensional Euclidean space is introduced, which are called shape-driven nested Markov tessellations. Locally, these…
Scale functions play a central role in the fluctuation theory of spectrally negative L\'evy processes. For spectrally negative compound Poisson processes with positive drift, a new representation of the $q$-scale functions in terms of the…
We identify q-deformed gl(l+1)-Whittaker functions with a specialization of Macdonald polynomials. This provides a representation of q-deformed gl(l+1)-Whittaker functions in terms of Demazure characters of affine Lie algebra \hat{gl(l+1)}.…
An approach for $q$-deformed Bogoliubov transformations is presented. Assuming a left-right module action together with an *-operation and deformed commutation relations, we construct a q-deformation of the nonlinear Bogoliubov…