相关论文: Double variational principle for mean dimension

A simple proof of the convergence of the variational regularization, with the regularization parameter, chosen by the discrepancy principle, is given for linear operators under suitable assumptions. It is shown that the discrepancy…

The rate-distortion dimension (RDD) of an analog stationary process is studied as a measure of complexity that captures the amount of information contained in the process. It is shown that the RDD of a process, defined as two times the…

We establish via variational methods the existence of a standing wave together with an estimate on the convergence to its asymptotic states for a bistable system of partial differential equations on a periodic domain. The main tool is a…

We show that dimensional theoretical properties of dynamical systems can considerably change because of number theoretical peculiarities of some parameter values

We study random domino tilings of a multiply-connected domain with a height function defined on the universal covering space of the domain. We prove a large deviation principle for the height function in two asymptotic regimes. The first…

We study the behavior of dynamical systems under time reparameterizations, which is important not only to characterize chaos in relativistic systems but also to probe the invariance of dynamical quantities. We first show that time…

In this note, we uncover three connections between the metric distortion problem and voting methods and axioms from the social choice literature.

We present a generalization of the variational principle that is compatible with any Hamiltonian eigenstate that can be specified uniquely by a list of properties. This variational principle appears to be compatible with a wide range of…

We prove a maximal-type large deviation principle for dynamical systems with arbitrarily slow polynomial mixing rates. Also several applications, particularly to billiard systems, are presented.

Metric mean dimension is a geometric invariant of dynamical systems with infinite topological entropy. We relate this concept with the fractal structure of the phase space and the H\"older regularity of the map. Afterwards we improve our…

A classic approach in dynamical systems is to use particular geometric structures to deduce statistical properties, for example the existence of invariant measures with stochastic-like behaviour such as large deviations or decay of…

We study the detection of a sparse change in a high-dimensional mean vector as a minimax testing problem. Our first main contribution is to derive the exact minimax testing rate across all parameter regimes for $n$ independent, $p$-variate…

Metric mean dimension is a metric-depedent quantity to characterize the topological complexity of systems with infinite topological entropy. In this paper, we investigate metric mean dimension of factor maps. (1) We introduce three types of…

We introduce the notion of Feldman-Katok metric mean dimensions in this note. We show metric mean dimensions defined by different metrics coincide under weak tame growth of covering numbers, and establish variational principles for…

We study optimization problems in ergodic theory from the view point of minimax problems. We give minimax characterizations of maximum ergodic averages involving time averages. Our approach works for the abstract variational principle of…

For integrable systems in the sense of multidimensional consistency (MDC) we can consider the Lagrangian as a form, which is closed on solutions of the equations of motion. For 2-dimensional systems, described by partial difference…

In this paper, we establish $\mathcal B$-valued variational inequalities for differential operators, ergodic averages and symmetric diffusion semigroups under the condition that Banach space $\mathcal B$ has martingale cotype property.…

A key issue in dimension reduction of dissipative dynamical systems with spectral gaps is the identification of slow invariant manifolds. We present theoretical and numerical results for a variational approach to the problem of computing…

We develop a systematic theory for the critical phenomena with memory in all spatial dimensions, including $d<d_c$, $d=d_c$, and $d>d_c$, the upper critical dimension. We show that the Hamiltonian plays a unique role in dynamics and the…

The ergodic decomposition theorem is a cornerstone result of dynamical systems and ergodic theory. It states that every invariant measure on a dynamical system is a mixture of ergodic ones. Here we formulate and prove the theorem in terms…