5 papers
Strong law of large numbers for generalized operator means II
Zoltán Léka, Miklós Pálfia
In this paper we continue the investigation of generalizations of the strong law of large numbers to operator means which has been initiated in the earlier paper "Strong law of lar…
On the Wasserstein barycenter of positive definite operators
Sejong Kim, Vatsalkumar N. Mer, Miklós Pálfia
We extend the Bures-Wasserstein mean of positive definite matrices to the case of positive definite operators on a Hilbert space. This is done through its defining stationary point…
Gradient flows and a Trotter--Kato formula of semi-convex functions on CAT(1)-spaces
Shin-ichi Ohta, Miklós Pálfia
We generalize the theory of gradient flows of semi-convex functions on CAT(0)-spaces, developed by Mayer and Ambrosio--Gigli--Savaré, to CAT(1)-spaces. The key tool is the so-calle…
Discrete-time gradient flows and law of large numbers in Alexandrov spaces
Shin-ichi Ohta, Miklós Pálfia
We develop the theory of discrete-time gradient flows for convex functions on Alexandrov spaces with arbitrary upper or lower curvature bounds. We employ different resolvent maps i…
Algorithmic definition of means acting on positive numbers and operators
Miklos Palfia
Means are used in several applications from electronic engeneering to information theory, however there is no general theorem on how to extend a given M(x, y) mean function to mult…