相关论文: Double variational principle for mean dimension
We study generic holomorphic families of dynamical systems presenting problems of small divisors with fixed arithmetic. We prove that we have convergence for all parameter values or divergence everywhere except for an exceptional set in the…
We study the distributional properties of the linear discriminant function under the assumption of normality by comparing two groups with the same covariance matrix but different mean vectors. A stochastic representation for the…
A good generalization of the Euclidean dimension to disordered systems and non crystalline structures is commonly required to be related to large scale geometry and it is expected to be independent of local geometrical modifications. The…
We show that the maximum expected inner product between a random vector and the standard normal vector over all couplings subject to a mutual information constraint or regularization is equivalent to a truncated integral involving the…
Principal component analysis continues to be a powerful tool in dimension reduction of high dimensional data. We assume a variance-diverging model and use the high-dimension, low-sample-size asymptotics to show that even though the…
According to a conjecture of Lindenstrauss and Tsukamoto, a topological dynamical system $(X,T)$ is embeddable in the $d$-cubical shift $(([0,1]^{d})^{\mathbb{Z}},\ shift)$ if both its mean dimension and periodic dimension are strictly…
Let $X$ be a full-shift on the alphabet $[0, 1]^a$ and let $(Y, S)$ be an arbitrary dynamical system. We prove that any equivariant continuous map from $X$ to $Y$ has conditional metric mean dimension not less than $a-\mathrm{mdim}(Y, S)$.…
We study an analogue of the large deviation principle for mixed measures associated with a class of $\log$-concave probability measures whose densities depend on the gauge function of a convex body. For convex bodies in $\mathbb{R}^n$, we…
In this paper the variation principles from theoretical physics is considered that would describe the process of routing in computer networks. The total traffic which is currently served on all hops of the route has been chosen as the…
We consider a system of diffusion processes that interact through their empirical mean and have a stabilizing force acting on each of them, corresponding to a bistable potential. There are three parameters that characterize the system: the…
This work focus on the large deviation principle for a two-time scale McKean-Vlasov system with jumps. Based on the variational framework of the McKean-Vlasov system with jumps, it is turned into weak convergence for the controlled system.…
Fluctuations in the return time statistics of a dynamical system can be described by a new spectrum of dimensions. Comparison with the usual multifractal analysis of measures is presented, and difference between the two corresponding sets…
We consider a two-dimensional Hamiltonian system perturbed by a small diffusion term, whose coefficient is state-dependent and non-degenerate. As a result, the process consists of the fast motion along the level curves and slow motion…
The purpose of the dynamics of moving systems is to search for the mathematical model that describes the link between the resultant applied force, that is the cause, and the speed of system that is the effect. This mathematical link…
Consider the stochastic differential equation in $\rr^d$ dX^{\e}_t&=b(X^{\e}_t)dt+\sqrt{\e}\sigma(X^\e_t)dB_t X^{\e}_0&=x_0,\quad x_0\in\rr^d$ where $b:\rr^d\to\rr^d$ is $C^1$ such that $<x,b(x)> \leq C(1+|x|^2)$, $\sigma:\rr^d\to…
We develop a general mathematical framework for variational problems where the unknown function assumes values in the space of probability measures on some metric space. We study weak and strong topologies and define a total variation…
Time-invariant linear dynamical system arises in many real-world applications,and its usefulness is widely acknowledged. A practical limitation with this model is that its latent dimension that has a large impact on the model capability…
Given two high-dimensional Gaussians with the same mean, we prove a lower and an upper bound for their total variation distance, which are within a constant factor of one another.
We characterize the rate-distortion function for zero-mean stationary Gaussian sources under the MSE fidelity criterion and subject to the additional constraint that the distortion is uncorrelated to the input. The solution is given by two…
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…