相关论文: Non-recurrence and divergent $\bf ({p(n)},{q(n)})$…

We show that for every "locally finite" unit-preserving completely positive map P acting on a C*-algebra, there is a corresponding *-automorphism \alpha of another unital C*-algebra such that the two sequences P, P^2,P^3,... and \alpha,…

The goal of this paper is to generalize, refine, and improve results on large intersections. We show that if $G$ is a countable abelian group and $\varphi, \psi : G \to G$ are homomorphisms such that at least two of the three subgroups…

It is well-known that there exist infinite sequences that are the fixed point of non-uniform morphisms, but not $k$-automatic for any $k$. In this note we show that every $k$-automatic sequence is the image of a fixed point of a {\it…

We investigate pointwise convergence of entangled ergodic averages of Dunford-Schwartz operators $T_0,T_1,\ldots, T_m$ on a Borel probability space. These averages take the form \[ \frac{1}{N^k}\sum_{1\leq n_1,\ldots, n_k\leq N}…

We prove gap theorems for entropy norms on automorphism groups of K3 surfaces, Enriques surfaces, and irreducible holomorphic symplectic manifolds. We also study the achirality of automorphisms of K3 surfaces and Enriques surfaces in terms…

Let $T_1, ..., T_l: X \to X$ be commuting measure-preserving transformations on a probability space $(X, \X, \mu)$. We show that the multiple ergodic averages $\frac{1}{N} \sum_{n=0}^{N-1} f_1(T_1^n x) ... f_l(T_l^n x)$ are convergent in…

For any measure preserving system $(X,\mathcal{X},\mu,T)$ and $A\in\mathcal{X}$ with $\mu(A)>0$, we show that there exist infinitely many primes $p$ such that $\mu\bigl(A\cap T^{-(p-1)}A\cap T^{-2(p-1)}A\bigr) > 0$ (the same holds with…

Nonstandard ergodic averages can be defined for a measure-preserving action of a group on a probability space, as a natural extension of classical (nonstandard) ergodic averages. We extend the one-dimensional theory, obtaining L^1 pointwise…

The entropy of an ergodic source is the limit of properly rescaled 1-block entropies of sources obtained applying successive non-sequential recursive pairs substitutions (see P. Grassberger 2002 ArXiv:physics/0207023 and D. Benedetto, E.…

Let $E\subset \mathbb Z$ be a set of positive upper density. Suppose that $P_1,P_2,..., P_k\in \mathbb Z[X]$ are polynomials having zero constant terms. We show that the set $E\cap (E-P_1(p-1))\cap ... \cap (E-P_k(p-1))$ is non-empty for…

In order to complete (and generalize) results of Gardiner and Praeger on 4-valent symmetric graphs (European J. Combin, 15 (1994)) we apply the method of lifting automorphisms in the context of elementary-abelian covering projections. In…

This paper explores the proof by J. Bourgain, H. Furstenberg, Y. Katznelson and D.S. Ornstein of their return times theorem [2] and lights a corner in it regarding the role of auto-correlation. As for pointwise convergence, this was already…

Let $(X,\mu)$ be a probability space equipped with an invertible, measure-preserving transformation $T\colon X \to X$. We exhibit a wide class of weights $w$ so that whenever $f,g \in L^{\infty}(X)$, the bilinear ergodic averages \[…

In this paper we consider a random graph on which topological restrictions are imposed, such as constraints on the total number of edges, wedges, and triangles. We work in the dense regime, in which the number of edges per vertex scales…

We show that the only random orderings of finite graphs that are invariant under isomorphism and induced subgraph are the uniform random orderings. We show how this implies the unique ergodicity of the automorphism group of the random…

We study the variation of the trace of the Frobenius endomorphism associated to a cyclic trigonal curve of genus g over a field of q elements as the curve varies in an irreducible component of the moduli space. We show that for q fixed and…

We prove quenched versions of a central limit theorem, a large deviations principle as well as a local central limit theorem for expanding on average cocycles. This is achieved by building an appropriate modification of the spectral method…

In this paper we combine the general tools developed in (arXiv:0905.0518) with several ideas taken from earlier work on one-dimensional nonconventional ergodic averages by Furstenberg and Weiss, Host and Kra and Ziegler to study the…

We study mixing properties of epimorphisms of a compact connected finite-dimensional abelian group $X$. In particular, we show that a set $F$, $|F|>\dim X$, of epimorphisms of $X$ is mixing iff every subset of $F$ of cardinality $(\dim…

Let $T$ be the Koopman operator of a measure preserving transformation $\theta$ of a probability space $(X,\Sigma,\mu)$. We study the convergence properties of the averages $M_nf:=\frac1n\sum_{k=0}^{n-1}T^kf$ when $f \in L^r(\mu)$, $0<r<1$.…