Transportation-cost inequality on path spaces with uniform distance

Transportation-Cost Inequalities on Path Space over Manifolds with Boundary

Let L = ∆ + Z for a C vector field Z on a complete Riemannian manifold possibly with a boundary. A number of transportation-cost inequalities on the path space for the (reflecting) L-diffusion process are proved to be equivalent to the curvature condition Ric−∇Z ≥ −K and the convexity of the boundary (if exists). These inequalities are new even for manifolds without boundary, and are partly ext...

Path Symmetries in Undirected Uniform-Cost Grids

We explore a symmetry-based reformulation technique which can speed up optimal pathfinding on undirected uniform-cost grid maps by over 30 times. Our offline approach decomposes grid maps into a set of empty rectangles, removing from each all interior nodes and possibly some from along the perimeter. We then add macro-edges between selected pairs of remaining perimeter nodes to facilitate prova...

Efficient Minimum Cost Matching and Transportation Using the Quadrangle Inequality

On statistical type convergence in uniform spaces

The concept of ${mathscr{F}}_{st}$-fundamentality is introduced in uniform spaces, generated by some filter ${mathscr{F}}$. Its equivalence to the concept of ${mathscr{F}}$-convergence in uniform spaces is proved. This convergence generalizes many kinds of convergence, including the well-known statistical convergence.

A Criterion for Talagrand’s Quadratic Transportation Cost Inequality

Abstract. We show that the quadratic transportation cost inequality T2 is equivalent to both a Poincaré inequality and a strong form of the Gaussian concentration property. The main ingredient in the proof is a new family of inequalities, called modified quadratic transportation cost inequalities in the spirit of the modified logarithmic-Sobolev inequalities by Bobkov and Ledoux [6], that are s...