1 citations · 1 across the 6 of their papers we have counts for
6 papers
Graphon Spin Systems as Exactly Solvable Models
Artem Alexandrov, Georgi S. Medvedev
Graphons are measurable functions used to describe the asymptotic behavior of convergent graph families. Originally motivated by problems in combinatorics and graph theory, graphon…
Interacting dynamical systems on networks and fractals: discrete and continuous models, mean-field limit, and convergence rates
Georgi S. Medvedev
We develop a continuum limit and mean-field theory for interacting particle systems (IPS) on self-similar networks, a new class of discrete models whose large-scale behavior gives…
Phase transitions in the Ising model on random graphs
Artem Alexandrov, Georgi S. Medvedev
We study phase transitions in the Ising model on random graphs using graph limits. We show that the critical temperatures are determined by the eigenvalues of the kernel operator a…
Graphon Signal Processing for Spiking and Biological Neural Networks
Takuma Sumi, Georgi S. Medvedev
Graph Signal Processing (GSP) extends classical signal processing to signals defined on graphs, enabling filtering, spectral analysis, and sampling of data generated by networks of…
The Large Deviation Principle for -random spectral measures
Mahya Ghandehari, Georgi S. Medvedev
The -random graphs provide a flexible framework for modeling large random networks. Using the Large Deviation Principle (LDP) for -random graphs from [9], we prove the LDP fo…
Bursting oscillations induced by small noise
Pawel Hitczenko, Georgi S. Medvedev
We consider a model of a square-wave bursting neuron residing in the regime of tonic spiking. Upon introduction of small stochastic forcing, the model generates irregular bursting.…