Related papers: Mixing on Stochastic Staircase Transformations
We construct a novel class of stochastic blockmodels using Bayesian nonparametric mixtures. These model allows us to jointly estimate the structure of multiple networks and explicitly compare the community structures underlying them, while…
There are familiar examples of computable structures having various computable Scott ranks. There are also familiar structures, such as the Harrison ordering, which have Scott rank $\omega_1^{CK}+1$. Makkai produced a structure of Scott…
We review and extend previous results on coincidence of mesh patterns. We introduce the notion of a force on a permutation pattern and apply it to the coincidence classification of mesh patterns, completing the classification up to size…
We give a fairly complete characterization of the exact components of a large class of uniformly expanding Markov maps of $\mathbb{R}$. Using this result, for a class of $\mathbb{Z}$-invariant maps and finite modifications thereof, we prove…
We construct new monomorphisms between mapping class groups of surfaces. The first family of examples injects the mapping class group of a closed surface into that of a different closed surface. The second family of examples are defined on…
To every local complete intersection ring one may associate a so-called generic hypersurface. In this paper we introduce rank varieties for modules and complexes over the generic hypersurface. The definition uses extension of scalars,…
We prove that for infinite rank-one transformations satisfying a property called "partial boundedness," the only commuting transformations are powers of the original transformation. This shows that a large class of infinite…
This paper uses a construction of M. Keane to show that there exists a topologically mixing interval exchange transformation.
We introduce a construction turning some Coxeter and Davis realizations of buildings into systolic complexes. Consequently groups acting geometrically on buildings of triangle types distinct from $(2,4,4)$, $(2,4,5)$, $(2,5,5)$, and various…
The cosine transforms of functions on the unit sphere play an important role in convex geometry, the Banach space theory, stochastic geometry and other areas. Their higher-rank generalization to Grassmann manifolds represents an interesting…
The note is devoted to multiple mixing, spectrum, rank and self-joinings of measure-preserving transformations. We recall famous open problems, discuss related questions and some known results. A hypothetical example of an automorphism of…
We give a general constructive proof for hierarchical coordinatizations (Lagrange Decompositions) of permutation groups. The generalization originates from the investigation of how the subgroup chains of finite permutation groups yield…
We consider Markov chains on general state spaces in stationary random environment which are defined by a random mapping that is contractive up to a bounded perturbation. We prove their convergence to a limiting law, providing convergence…
Since 1997 a considerable effort has been spent to study the mixing time of switch Markov chains on the realizations of graphic degree sequences of simple graphs. Several results were proved on rapidly mixing Markov chains on unconstrained,…
New identities and congruences involving the ranks and cranks of partitions are proved. The proof depends on a new partial differential equation connecting their generating functions.
We slightly extend the convex integration via staircase laminate toolbox recently developed by Kleiner, M\"uller, Sz\'{e}kelyhidi, and Xie. As an example we revisit the proof by Astala-Faraco-Sz\'{e}kelyhidi on optimal Meyers' regularity…
We introduce the concept of deck transformations within the category of developable complexes of groups. Drawing inspiration from classical covering theory for topological spaces, we propose an alternative construction of the universal…
We give unique recovery guarantees for matrices of bounded rank that have undergone permutations of their entries. We even do this for a more general matrix structure that we call ladder matrices. We use methods and results of commutative…
The paper deals with the problem of long-time asymptotic behaviour of solutions for classes of ODEs and PDEs, perturbed by stationary noises. The latter are not assumed to be $\delta$-correlated in time, so that the evolution in question is…
For Markov chains and Markov processes exhibiting a form of stochastic monotonicity (larger states shift up transition probabilities in terms of stochastic dominance), stability and ergodicity results can be obtained using order-theoretic…