相关论文: Intertwining and commutation relations for birth-d…
A stochastic comparison result that makes progress towards understanding the classical multitype contact process with unequal death rates is given. It has long been conjectured that the particle type with the largest birth to death rate…
The conjecture of Valent about the type of Jacobi matrices with polynomially growing weights is proved.
Birth-and-death processes are widely used to model the development of biological populations. Although they are relatively simple models, their parameters can be challenging to estimate, because the likelihood can become numerically…
In a recent paper in the Journal of Theoretical Probability Gong, Mao and Zhang, using the theory of Dirichlet forms, extended Karlin and McGregor's classical results on first-hitting times of a birth-death process on the nonnegative…
Fermions coupled to Yang-Mills matrix models are studied from the point of view of emergent gravity. We show that the simple matrix model action provides an appropriate coupling for fermions to gravity, albeit with a non-standard spin…
We consider the Poisson equation $(I-P)\boldsymbol{u}=\boldsymbol{g}$, where $P$ is the transition matrix of a Quasi-Birth-and-Death (QBD) process with infinitely many levels, $\bm g$ is a given infinite dimensional vector and $\bm u$ is…
The main goal of this note is to suggest an algebraic approach to the quasi-isometric classification of partially commutative groups (alias right-angled Artin groups). More precisely, we conjecture that if the partially commutative groups…
We prove a new kind of quantum de Finetti theorem for representations of the unitary group U(d). Consider a pure state that lies in the irreducible representation U_{mu+nu} for Young diagrams mu and nu. U_{mu+nu} is contained in the tensor…
Many spatio-temporal data record the time of birth and death of individuals, along with their spatial trajectories during their lifetime, whether through continuous-time observations or discrete-time observations. Natural applications…
The late-time dynamics of quantum many-body systems is organized in distinct dynamical universality classes, characterized by their conservation laws and thus by their emergent hydrodynamic transport. Here, we study transport in the…
For different reversible Markov kernels on finite state spaces, we look for families of probability measures for which the time evolution almost remains in their convex hull. Motivated by signal processing problems and metastability studies…
In a recent series of papers we have analyzed a certain deformation of the canonical commutation relations producing an interesting functional structure which has been proved to have some connections with physics, and in particular with…
The usual position-momentum commutation relation plays a fundamental role in the mathematical description of continuous-variable quantum systems. In the case of a qudit described by a Hilbert space of a high enough dimension, there exists a…
We consider elliptic diffusion processes on $\mathbb R^d$. Assuming that the drift contracts distances outside a compact set, we prove that, at a sufficiently high temperature, the Markov semi-group associated to the process is a…
We consider Poisson's equation for quasi-birth-and-death processes (QBDs) and we exploit the special transition structure of QBDs to obtain its solutions in two different forms. One is based on a decomposition through first passage times to…
Permutation and its partial transpose play important roles in quantum information theory. The Werner state is recognized as a rational solution of the Yang--Baxter equation, and the isotropic state with an adjustable parameter is found to…
We find new solutions to the Yang--Baxter equation in terms of the intertwiner matrix for semi-cyclic representations of the quantum group $U_q(s\ell(2))$ with $q= e^{2\pi i/N}$. These intertwiners serve to define the Boltzmann weights of a…
We develop a general theory of intertwined diffusion processes of any dimension. Our main result gives an SDE construction of intertwinings of diffusion processes and shows that they correspond to nonnegative solutions of hyperbolic partial…
A review is given on the subject of hadron production at intermediate $p_T$ in heavy-ion collisions. The underlying dynamical processes are inferred from interpreting the data in the framework of recombination. Ridge formation with or…
We emphasize intertwining relations as a universal tool in constructing one-dimensional quasi-exactly solvable operators and offer their possible generalization to the multidimensional case. Considered examples include all quasi-exactly…