5 papers
Ultrametric Graphons and Hierarchical Community Networks: Spectral Theory and Applications
Ángel Alfredo Morán Ledezma
We develop a theory of ultrametric graphons as limiting objects for random networks with nested hierarchical community structure. A graphon is called ultrametri…
Dynamic centrality of headwater sources in river networks: a stochastic approach via ultrametric Laplacians
Ángel Alfredo Morán Ledezma
River networks are hierarchical transport systems in which the timing and position of headwater confluences govern hydrologic response, solute transport, and ecological connectivit…
Spectral Geometry and Heat Kernels on Phylogenetic Trees
Ángel Alfredo Morán Ledezma
We develop a unified spectral framework for finite ultrametric phylogenetic trees, grounding the analysis of phylogenetic structure in operator theory and stochastic dynamics in th…
A non-autonomous p-Adic diffusion equation on time changing graphs
Patrick Erik Bradley, Ángel Morán Ledezma
Motivated by the recently proven presence of ultrametricity in physical models (certain spin glasses) and the very recent study of Turing patterns on locally ultrametric state spac…
A probabilistic interpretation of Weil's explicit sums and arithmetic spectral measures
Ángel Alfredo Morán Ledezma
In this paper we study the connections of three paradigms in number theory: the adelic formulation of the Riemann zeta function, the Weil explicit formula and the concepts of the s…