14 citations · 37 across the 20 of their papers we have counts for
20 papers
Rigidity and equidistribution of random walks by diffeomorphisms near the conservative regime
Timothée Bénard, Zhiyuan Zhang
We consider a random walk on a closed manifold driven by a probability measure on the space of diffeomorphisms. Provided has compact support, satisfies certain ga…
Ergodicity of (co)expanding on average random dynamical systems
Jonathan DeWitt, Dmitry Dolgopyat, Zhiyuan Zhang
We prove ergodicity for random dynamics satisfying some expansion and irreducibility conditions. As a particular application, we show that if , $d\ge 2…
Spectral conditions for forbidden subgraphs in bipartite graphs
Yuan Ren, Jing Zhang, Zhiyuan Zhang
A graph is -free, if it contains no as a subgraph. A graph is said to be \emph{-minor free}, if it does not contain as a minor. In recent years, Nikiforov asked t…
Geometric properties of partially hyperbolic measures and applications to measure rigidity
Alex Eskin, Rafael Potrie, Zhiyuan Zhang
We give a geometric characterization of the quantitative non-integrability, introduced by Katz, of strong stable and unstable bundles of partially hyperbolic measures and sets in d…
On pseudo-rotations of the annulus with generic rotation number
Barney Bramham, Zhiyuan Zhang
We show that for a Baire generic rotation number , the set of area preserving -pseudo-rotations of the annulus with rotation nu…
On bifurcation of statistical properties of partially hyperbolic endomorphisms
Masato Tsujii, Zhiyuan Zhang
We give an example of a path-wise connected open set of partially hyperbolic endomorphisms on the -torus, on which the SRB measure exists for each system and varies s…
Maximal parahoric arithmetic transfers, resolutions and modularity
Zhiyu Zhang
For any unramified quadratic extension of -adic local fields , we formulate several arithmetic transfer conjectures at any maximal parahoric level, in the context…
A spectral condition for the existence of cycles with consecutive odd lengths in non-bipartite graphs
Zhiyuan Zhang, Yanhua Zhao
A graph is called -free, if it does not contain as a subgraph. In 2010, Nikiforov proposed a Brualdi-Solheid-Turán type problem: what is the maximum spectral radius of a…
Uniform Embeddings for Robinson Similarity Matrices
Jeannette Janssen, Zhiyuan Zhang
A Robinson similarity matrix is a symmetric matrix where the entry values on all rows and columns increase toward the diagonal. Decompose the Robinson matrix into the sum of k {0,…
Smooth mixing Anosov flows in dimension three are exponential mixing
Masato Tsujii, Zhiyuan Zhang
We show that a topologically mixing Anosov flow on a 3 dimensional compact manifold is exponential mixing with respect to any equilibrium measure with Holder potential.
Zimmer's conjecture for lattice actions: the -case
Zhiyuan Zhang
We prove Zimmer's conjecture for co-compact lattices in : for any co-compact lattice in , , any -action on a compact ma…
actions on manifolds by lattices in Lie groups
Aaron Brown, Danijela Damjanovic, Zhiyuan Zhang
In this paper we study Zimmer's conjecture for actions of lattice subgroup of a higher-rank simple Lie group with finite center on compact manifolds. We show that when the ra…
On topological genericity of the mode-locking phenomenon
Zhiyuan Zhang
We study the circle homeomorphisms extensions over a strictly ergodic homeomorphism. Under a very mild restriction, we show that the fibered rotation number is locally constant on…
The rigidity of pseudo-rotations on the two-torus and a question of Norton-Sullivan
Jian Wang, Zhiyuan Zhang
We show that under certain boundedness condition, a conservative irrational pseudo-rotations on with a generic rotation vector is -rigid. We also ob…
An effective version of Katok's horseshoe theorem for conservative surface diffeomorphisms
Bassam Fayad, Zhiyuan Zhang
For area preserving surface diffeomorphisms, we give an explicit finite information condition, on the exponential growth of the number of Bowen's balls needed to cove…
On stable transitivity of finitely generated groups of volume preserving diffeomorphisms
Zhiyuan Zhang
In this paper, we provide a new criterion for the stable transitivity of volume preserving finite generated group on any compact Riemannian manifold. As one of our applications, we…
On the smooth dependence of SRB measures for partially hyperbolic systems
Zhiyuan Zhang
In this paper, we study the differentiability of SRB measures for partially hyperbolic systems. We show that for any , for any integer , any sufficiently lar…
Ballistic Transport and Absolute Continuity of One-Frequency Schrödinger Operators
Zhiyuan Zhang, Zhiyan Zhao
For the solution to the discrete Schrödinger equation with $α\in\R\setminus\Q$ and $V\in…
prevalence of stable ergodicity for a class of partially hyperbolic systems
Martin Leguil, Zhiyuan Zhang
We prove that for , for any dynamically coherent, center bunched and strongly pinched volume preserving partially hyperbolic diffeo…
On the spectrums of ergodic Schrodinger operators with finitely valued potentials
Zhiyuan Zhang
We show that the measure of the spectrum of Schrödinger operator with potential defined by non-constant function over any minimal aperiodic finite subshift tends to zero, as the co…