Related papers: On mixing and the local central limit theorem for …
We prove central and local limit theorems for random walks on the Poincar{\'e} hyperbolic space of dimension n {\v e} 2. To this end we use the ball model and describe the walk therein through the M{\"o}bius addition and multiplication.…
We introduce a local version of contact homology for an isolated periodic orbit of the Reeb flow and prove that its rank is uniformly bounded for isolated iterations. Several applications are obtained, including a generalization of…
This paper establishes limit theorems for a class of stochastic hybrid systems (continuous deterministic dynamic coupled with jump Markov processes) in the fluid limit (small jumps at high frequency), thus extending known results for jump…
We prove that the projective complex algebraic varieties admitting a large complex local system satisfy a strong version of the Green-Griffiths-Lang conjecture.
In this article we consider the inhomogeneous incompressible Euler equations describing two fluids with different constant densities under the influence of gravity as a differential inclusion. By considering the relaxation of the…
We introduce a coarse flow space for relatively hyperbolic groups and use it to verify a regularity condition for the action of relatively hyperbolic groups on their boundaries. As an application the Farrell-Jones Conjecture for relatively…
We study an initial boundary value problem for the Navier-Stokes equations of compressible viscous heat-conductive fluids in a 2-D periodic domain or the unit square domain. We establish a blow-up criterion for the local strong solutions in…
In this work, we consider the problem of event-triggered implementation of control laws designed for the local stabilization of nonlinear systems with center manifolds. We propose event-triggering conditions which are derived from a local…
We consider a $C^1$ neighborhood of the time-one map of a hyperbolic flow and prove that the topological entropy varies continuously for diffeomorphisms in this neighborhood. This shows that the topological entropy varies continuously for…
We derive new bounds of the remainder in a combinatorial central limit theorem without assumptions on independence and existence of moments of summands. For independent random variables our theorems imply Esseen and Berry-Esseen type…
In this paper, a new type of comparison theorem is presented for some initial-boundary value problems of second order nonlinear parabolic systems with nonlinear boundary conditions. This comparison theorem has an advantage over the…
We obtain central limit theorem, local limit theorems and renewal theorems for stationary processes generated by skew product maps $T(\om,x)=(\te\om,T_\om x)$ together with a $T$-invariant measure, whose base map $\te$ satisfies certain…
We consider a geodesic billiard system consisting of a complete Riemannian manifold and an obstacle submanifold with boundary at which the trajectories of the geodesic flow experience specular reflections. We show that if the geodesic…
We establish an improved criterion for rapid mixing of hyperbolic flows by weakening the requirement on the temporal distance function from positive box dimension to the existence of two values whose ratio is Diophantine. We also…
We investigate the issue of uniqueness of the limit flow for a relevant class of quasi-linear parabolic equations defined on the whole space. More precisely, we shall investigate conditions which guarantee that the global solutions decay at…
In this paper, we consider a hydrodynamic $Q$-tensor system for nematic liquid crystal flow, which is derived from Doi-Onsager molecular theory by the Bingham closure. We first prove the existence and uniqueness of local strong solution.…
We study dynamical systems arising as time-dependent compositions of Pomeau-Manneville-type intermittent maps. We establish central limit theorems for appropriately scaled and centered Birkhoff-like partial sums, with estimates on the rate…
In dilute suspensions of swimming microorganisms the local fluid velocity is a random superposition of the flow fields set up by the individual organisms, which in turn have multipole contributions decaying as inverse powers of distance…
We show that molecular dynamics simulations can furnish useful boundary conditions at a solid surface bounding a two-component fluid. In contrast to some previous reports, convective-diffusive flow is consistent with continuum equations…
We investigate a wide class of two-dimensional hyperbolic systems with singularities, and prove the almost sure invariance principle (ASIP) for the random process generated by sequences of dynamically H\"older observables. The observables…