Uniform Contractivity in Wasserstein Metric for the Original 1D Kac’s Model
نویسندگان
چکیده
منابع مشابه
Convergence in the Wasserstein Metric for MarkovChain
This paper gives precise bounds on the convergence time of the Gibbs sampler used in the Bayesian restoration of a degraded image. Convergence to stationarity is assessed using the Wasserstein metric, rather than the usual choice of total variation distance. The Wasserstein metric may be more easily applied in some applications, particularly those on continuous state spaces. Bounds on convergen...
متن کاملThe Exponential Formula for the Wasserstein Metric
Many evolutionary partial differential equations may be rewritten as the gradient flow of an energy functional, a perspective which provides useful estimates on the behavior of solutions. The notion of gradient flow requires both the specification of an energy functional and a metric with respect to which the gradient is taken. In recent years, there has been significant interest in gradient fl...
متن کاملThe Wasserstein-Fisher-Rao metric
This note gives a summary of the presentation that I gave at the workshop on shape analysis. Based on [CSPV15, CPSV15], we present a generalization of optimal transport to measures that have different total masses. This generalization enjoys most of the properties of standard optimal transport but we will focus on the geometric formulation of the model. We expect this new metric to have interes...
متن کاملThe Wasserstein metric in Factor Analysis
We consider the problem of approximating a (nonnegative definite) covariance matrix by the sum of two structured covariances –one which is diagonal and one which has low-rank. Such an additive decomposition follows the dictum of factor analysis where linear relations are sought between variables corrupted by independent measurement noise. We use as distance the Wasserstein metric between their ...
متن کاملStrict Contractivity of the 2-wasserstein Distance for the Porous Medium Equation by Mass-centering
We show that the Euclidean Wasserstein distance between two compactly supported solutions of the one–dimensional porous medium equation having the same center of mass decays to zero for large times. As a consequence, we detect an improved L1–rate of convergence of solutions of the one–dimensional porous medium equation towards well–centered self–similar Barenblatt profiles, as time goes to infi...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Statistical Physics
سال: 2016
ISSN: 0022-4715,1572-9613
DOI: 10.1007/s10955-016-1476-1