## Radu Mardare ; Prakash Panangaden ; Gordon D. Plotkin - Free complete Wasserstein algebras

lmcs:4312 - Logical Methods in Computer Science, September 14, 2018, Volume 14, Issue 3 - https://doi.org/10.23638/LMCS-14(3:19)2018
Free complete Wasserstein algebras

We present an algebraic account of the Wasserstein distances $W_p$ on complete metric spaces, for $p \geq 1$. This is part of a program of a quantitative algebraic theory of effects in programming languages. In particular, we give axioms, parametric in $p$, for algebras over metric spaces equipped with probabilistic choice operations. The axioms say that the operations form a barycentric algebra and that the metric satisfies a property typical of the Wasserstein distance $W_p$. We show that the free complete such algebra over a complete metric space is that of the Radon probability measures with finite moments of order $p$, equipped with the Wasserstein distance as metric and with the usual binary convex sums as operations.

Volume: Volume 14, Issue 3
Published on: September 14, 2018
Accepted on: September 14, 2018
Submitted on: February 24, 2018
Keywords: Computer Science - Logic in Computer Science