## Journals

- Advances in Mathematics of Communications
- Big Data & Information Analytics
- Communications on Pure & Applied Analysis
- Discrete & Continuous Dynamical Systems - A
- Discrete & Continuous Dynamical Systems - B
- Discrete & Continuous Dynamical Systems - S
- Evolution Equations & Control Theory
- Inverse Problems & Imaging
- Journal of Computational Dynamics
- Journal of Dynamics & Games
- Journal of Geometric Mechanics
- Journal of Industrial & Management Optimization
- Journal of Modern Dynamics
- Kinetic & Related Models
- Mathematical Biosciences & Engineering
- Mathematical Control & Related Fields
- Mathematical Foundations of Computing
- Networks & Heterogeneous Media
- Numerical Algebra, Control & Optimization
- Electronic Research Announcements
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- AIMS Mathematics

DCDS

In this work, we show that a family of non-linear
mean-field equations on discrete spaces can be viewed as a gradient
flow of a natural free energy functional with respect to a certain
metric structure we make explicit. We also prove that this gradient
flow structure arises as the limit of the gradient flow structures
of a natural sequence of $N$-particle dynamics, as $N$ goes to
infinity.

DCDS

We establish an improved form of the classical logarithmic Sobolev inequality for the Gaussian
measure restricted to probability densities which satisfy a Poincaré inequality.
The result implies a lower bound
on the deficit in terms of the quadratic Kantorovich-Wasserstein distance. We similarly investigate
the deficit in the Talagrand quadratic transportation cost inequality this time by means of an
${ L}^1$-Kantorovich-Wasserstein distance, optimal for product measures, and deduce a lower bound on the deficit in the logarithmic Sobolev inequality in terms of this metric. Applications are given in the context
of the Bakry-Émery theory and the coherent state transform. The proofs combine tools from
semigroup and heat kernel theory and optimal mass transportation.

## Year of publication

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