相关论文: Recurrence rate in rapidly mixing dynamical system…

Let $\Lambda$ be a countable index set and $S=\{\phi_i: i\in \Lambda\}$ be a conformal iterated function system on $[0,1]^d$ satisfying the open set condition. Denote by $J$ the attractor of $S$. With each sequence $(w_1,w_2,...)\in…

The quantum form of the Poincar\'e recurrence theorem stipulates that a system with a time-independent Hamiltonian and discrete energy levels returns arbitrarily close to its initial state in a finite time. Qubit systems, being highly…

For a class of interacting particle systems in continuous space, we show that finite-volume approximations of the bulk diffusion matrix converge at an algebraic rate. The models we consider are reversible with respect to the Poisson…

The recurrence features of persistent random walks built from variable length Markov chains are investigated. We observe that these stochastic processes can be seen as L{\'e}vy walks for which the persistence times depend on some internal…

Let $(X,\mu,T_1,...,T_l)$ be a measure-preserving system with those $T_i$ are commuting. Suppose that the polynomials $p_1(t),...,p_{l}(t)\in\Z[t]$ with $p_j(0)=0$ have distinct degrees. Then for any $\epsilon>0$ and $A\subseteq X$ with…

We consider a stochastic particle system in which a finite number of particles interact with one another via a common energy tank. Interaction rate for each particle is proportional to the square root of its kinetic energy, as is consistent…

We extend the close interplay between continued fractions, orthogonal polynomials, and Gaussian quadrature rules to several variables in a special but natural setting which we characterize in terms of moment sequences. The crucial condition…

Persistence diagrams, combining geometry and topology for an effective shape description used in pattern recognition, have already proven to be an effective tool for shape representation with respect to a certainfiltering function.…

Quantum states inevitably decay with time into a probabilistic mixture of classical states, due to their interaction with the environment and measurement instrumentation. We present the first measurement of the decoherence dynamics of…

We investigate the structure of return-time sets determined by orbits along polynomial tuples in minimal topological dynamical systems. Building on the topological characteristic factor theory of Glasner, Huang, Shao, Weiss, and Ye, we…

We investigate the relations holding among generalized dimensions of invariant measures in dynamical systems and similar quantities defined by the scaling of global averages of powers of return times. Because of a heuristic use of Kac…

Recurrence plot based time series analysis is widely used to study changes and transitions in the dynamics of a system or temporal deviations from its overall dynamical regime. However, most studies do not discuss the significance of the…

We present a theory and accompanying importance sampling method for computing rate constants in spatially inhomogenious systems. Using the relationship between rate constants and path space partition functions, we illustrate that the…

Two quantitative notions of mixing are the decay of correlations and the decay of a mix-norm -- a negative Sobolev norm -- and the intensity of mixing can be measured by the rates of decay of these quantities. From duality, correlations are…

We consider the minimal distance between orbits of measure preserving dynamical systems. In the spirit of dynamical shrinking target problems we identify distance rates for which almost sure asymptotic closeness properties can be ensured.…

Ab initio predictions of two-loop electroweak contributions to observables are increasingly essential for precision collider experiments, yet their evaluation remains very challenging. We connect recurrence techniques and dispersive method…

We study the monic orthogonal polynomials with respect to a singularly perturbed Airy weight. By using Chen and Ismail's ladder operator approach, we derive a discrete system satisfied by the recurrence coefficients for the orthogonal…

Over the last decade it has become clear that discrete Painlev\'e equations appear in a wide range of important mathematical and physical problems. Thus, the question of recognizing a given non-autonomous recurrence as a discrete Painlev\'e…

In this paper we present a general scheme for how to relate differential equations for the recurrence coefficients of semi-classical orthogonal polynomials to the Painlev\'e equations using the geometric framework of the Okamoto Space of…

The eigenvalue density of a quantum-mechanical system exhibits oscillations, determined by the closed orbits of the corresponding classical system; this relationship is simple and strong for waves in billiards or on manifolds, but becomes…