Related papers: A shadow Markov equation
In the hidden Markov process, there is a possibility that two different transition matrices for hidden and observed variables yield the same stochastic behavior for the observed variables. Since such two transition matrices cannot be…
A new relativistic invariant version of nonlinear Maxwell equations is offerred. Some properties of these equations are considered.
The probabilistic description of finite classical systems often leads to linear kinetic equations. A set of physically motivated mathematical requirements is accordingly formulated. We show that it necessarily implies that solutions of such…
We establish an equivalence-singularity dichotomy for a large class of one-dimensional Markov measures. Our approach is new in that we deal with one-sided and two-sided chains simultaneously, and in that we do not appeal to any 0-1 law. In…
This is an attempt to find a hidden virtue in Tolman's paradox by showing that it can give rise to quantum superposition. We consider tachyon exchange between two particles and show that it can generate superposition of eigenstates…
Under continuity and recurrence assumptions, we prove that the iteration of successive partial symmetrizations that form a time-homogeneous Markov process, converges to a symmetrization. We cover several settings, including the…
The pseudo-amenability of Brandt Banach semigroup algebras is considered.
We describe a Markov dilation for any weak* continuous semigroup $(T_t)_{t \geq 0}$ of selfadjoint unital completely positive Fourier multipliers acting on the group von Neumann algebra $\mathrm{VN}(G)$ of a locally compact group $G$.
Let g be a complex, semisimple Lie algebra. Drinfeld showed that the quantum group associated to g is isomorphic as an algebra to the trivial deformation of the universal enveloping algebra of g. In this paper we construct explicitly such…
We establish a simple variance inequality for U-statistics whose underlying sequence of random variables is an ergodic Markov Chain. The constants in this inequality are explicit and depend on computable bounds on the mixing rate of the…
In 1999, Khovanov showed that a link invariant known as the Jones polynomial is the Euler characteristic of a homology theory. The knot categorification problem is to find a general construction of knot homology groups, and to explain their…
Supersymmetry and Lorentz invariance are closely related as both are spacetime symmetries. Terms can be added to Lagrangians that explicitly break either supersymmetry or Lorentz invariance. It is possible to include terms which violate…
Given the real Clifford algebra of a quadratic space with a given signature, we define a new product in this structure such that it simulates the Clifford product of a quadratic space with another signature different from the original one.…
Closed geodesics associated with indefinite binary quadratic forms, or equivalently with real quadratic irrationals, have long been studied as geometric $\mathrm{SL}_2(\mathbb{Z})$-invariants. Building on the Birman-Williams approach to…
This is a survey article on some connections between cluster algebras and link invariants, written for the Notices of the AMS.
We consider a degenerate stochastic differential equation that has a sticky point in the Markov process sense. We prove that weak existence and weak uniqueness hold, but that pathwise uniqueness does not hold nor does a strong solution…
A new scaling variable is introduced in terms of which nuclear shadowing in deep-inelastic scattering is universal, i.e. independent of $A$, $Q^2$ and $x$. This variable can be interpreted as a measure of the number of gluons probed by the…
We show that the Drinfeld-Sokolov system of equations has a nontrivial prolongation structure. The closure process for prolongation algebra gives rise to the sl(4,c) algebra which is used to derive the scattering problem for the system of…
We study asymptotic behavior of a Markov semigroup on a von-Neumann algebra by exploring a maximal von-Neumann subalgebra where the Markov semigroup is an automorphism. This enables us to prove that strong mixing is equivalent to ergodic…
It is known that some cosmological perturbations are conformal invariant. This facilitates the studies of perturbations within some gravitational theories alternative to general relativity, for example the scalar-tensor theory, because it…