Related papers: Mixing on Stochastic Staircase Transformations
We investigate several categories related to transition structures, using a mixture of algebraic and topological methods. We show how two such categories are connected by a contravariant adjunction. This is the most detailed of a family of…
Using the correspondence between a cycle up-down permutation and a pair of matchings, we give a combinatorial proof of the enumeration of alternating permutations according to the given peak set.
The presence of higher-order interactions (simplicial complexes) in networks and certain types of multilayer networks has shown to lead to the abrupt first-order transition to synchronization. We discover that simplicial complexes on…
We establish necessary and sufficient conditions for suspension flows over certain families of shift spaces to be topologically mixing. We also show the similarities and differences between this case and the smooth measure theoretic setting…
Various topics in stochastic processes have been considered in the abstract setting of Riesz spaces, for example martingales, martingale convergence, ergodic theory, AMARTS, Markov processes and mixingales. Here we continue the relaxation…
We study topological mixing properties and the maximal equicontinuous factor of rank-one subshifts as topological dynamical systems. We show that the maximal equicontinuous factor of a rank-one subshift is finite. We also determine all the…
For a class of irrational numbers, depending on their Diophantine properties, we construct explicit rank-one transformations that are totally ergodic and not weakly mixing. We classify when the measure is finite or infinite. In the finite…
We study characterizations of ergodicity, weak mixing and strong mixing of W*-dynamical systems in terms of joinings and subsystems of such systems. Ergodic joinings and Ornstein's criterion for strong mixing are also discussed in this…
Motivated by an ongoing project on computer aided derivation of asymptotic models governed by partial differential equations, we introduce a class of term transformations that consists of traversal strategies and insertion of contexts. We…
We study the maximal rank in affine subspaces of symmetric or alternating matrices, in terms of the matching numbers of certain associated graphs. Applications include simple proofs of upper bounds on the dimension of such subspaces in…
We introduce a new tool to study the spectral type of rank one transformations using the method of central limit theorem for trigonometric sums. We get some new applications.
We introduce a lifting of West's stack-sorting map $s$ to partition diagrams, which are combinatorial objects indexing bases of partition algebras. Our lifting $\mathscr{S}$ of $s$ is such that $\mathscr{S}$ behaves in the same way as $s$…
We consider a new kind of straight and shifted plane partitions/Young tableaux --- ones whose diagrams are no longer of partition shape, but rather Young diagrams with boxes erased from their upper right ends. We find formulas for the…
In this paper, we further investigate the orthogonally connected sets and establish necessary and sufficient conditions for a set to be staircase connected.
We define the notion of canonical boundedness among rank-one transformations and use it to characterize the class of all bounded rank-one transformations with trivial centralizer. We also explicitly characterize totally ergodic rank-one…
We exploit a bijection between plane recursive trees and Stirling permutations; this yields the equivalence of some results previously proven separately by different methods for the two types of objects as well as some new results. We also…
Mixed superposition rules, i.e., functions describing the general solution of a system of first-order differential equations in terms of a generic family of particular solutions of first-order systems and some constants, are studied. The…
We study assortative mixing in networks, the tendency for vertices in networks to be connected to other vertices that are like (or unlike) them in some way. We consider mixing according to discrete characteristics such as language or race…
A unified approach to parametrization of the mixing matrix for $N$ generations is developed. This approach not only has a clear geometrical underpinning but also has the advantage of being economical and recursive and leads in a natural way…
In this paper some sufficient conditions are given for when two bounded rank-one transformations are isomorphic or disjoint. For commensurate, canonically bounded rank-one transformations, isomorphism and disjointness are completely…