Related papers: Constructing Proper Markov Semigroups for Arveson …
W. Arveson has described a cocycle conjugacy class $U(\alpha)$ of $E_0$-semigroup $\alpha$ on B(H) which is a factor of type $\rm I$. Under some conditions on $\alpha$, there is a $E_0$-semigroup $\beta \in U(\alpha)$ being a flow of shifts…
We study automaton structures, i.e. groups, monoids and semigroups generated by an automaton, which, in this context, means a deterministic finite-state letter-to-letter transducer. Instead of considering only complete automata, we…
This paper gives a complete classification of the possible ergodic decompositions for certain open families of volume-preserving partially hyperbolic diffeomorphisms. These families include systems with compact center leaves and…
We define tensor product decompositions of $E_0$-semigroups with a structure analogous to a classical theorem of Beurling. Such decompositions can be characterized by adaptedness and exactness of unitary cocycles. For CCR-flows we show that…
An $\mathcal{A}$-semigroup is a numerical semigroup without consecutive small elements. This work generalizes this concept to finite-complement submonoids of an affine cone $\mathcal{C}$. We develop algorithmic procedures to compute all…
It has been realized over the past two decades that topological nontriviality can be present not only in insulators but also in gapless semimetals, the most prominent example being Weyl semimetals in three dimensions. Key to topological…
As shown in [1], we reduce periodicity of fuzzy Markov chains using the Halton quasi-random generator. In this paper, we employ two different quasi-random sequences namely Faure and Kronecker to generate the membership values of fuzzy…
In the quest in constructing conformal field theories (CFT) Jones has discovered a beautiful and deep connection between CFT, Richard Thompson's groups and knot theory. This led to a powerful functorial framework for constructing actions 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…
We study a class of ergodic quantum Markov semigroups on finite-dimensional unital $C^*$-algebras. These semigroups have a unique stationary state $\sigma$, and we are concerned with those that satisfy a quantum detailed balance condition…
We construct explicitly a family of proper subgroups of the tame automorphism group of affine three-space (in any characteristic) which are generated by the affine subgroup and a non-affine tame automorphism. One important corollary is the…
In this paper we construct a conservative Markov semi-group with generator $L=\Delta+b\cdot\nabla$ on $\mathbb{R}^n$, where $b$ is a divergence-free vector field which belongs to $L^{2}\cap L^{p}$ with $\frac{n}{2}<p$. The research is…
A CP-semigroup is aligned if its set of trivially maximal subordinates is totally ordered by subordination. We prove that aligned spatial E_0-semigroups are prime: they have no non-trivial tensor product decompositions up to cocycle…
In this paper, we provide a complete description of congruence-semisimple semirings and introduce the pre-ordered abelian Grothendieck groups $K_0(S)$ and $SK_0(S)$ of the isomorphism classes of the finitely generated projective and…
Using a (1,1)-tensor L with zero Nijenhuis torsion and maximal possible number (equal to the number of dependent variables) of distinct, functionally independent eigenvalues we define, in a coordinate-free fashion, the seed systems which…
Using valuative techniques, we show that a smooth affine surface with a non-elementary automorphism group and completable by a cycle of rational curves is either the algebraic torus or a smooth cubic affine surface of Markov type.…
We show that labelled Thompson groups and twisted Brin--Thompson groups are all acyclic. This allows us to prove several new embedding results for groups. First, every group of type $F_n$ embeds quasi-isometrically as a subgroup of an…
Using Fedosov's approach we give a geometric construction of a formal symplectic groupoid over any Poisson manifold endowed with a torsion-free Poisson contravariant connection. In the case of Kaehler-Poisson manifolds this construction…
We characterize Markov lattice semigroups induced by measurable semiflows on probability spaces by properties of their generators. In addition we construct topological models on compact spaces for such semigroups.
We consider a stochastic electroconvection model describing the nonlinear evolution of a surface charge density in a two-dimensional fluid with additive stochastic forcing. We prove the existence and uniqueness of solutions, we define the…