Sublinearly reinforced Pólya urns on graphs of bounded degree
Master's thesis for the degree of Elite-M.Sc. in Theoretical and Mathematical Physics at the Ludwig Maximilian University of Munich and Technical University of Munich, 2018
No presentation slides are available, since it was done on the blackboard.
Abstract
Consider reinforced Pólya urns on the vertices of infinite graphs with bounded degree, where the edges of each vertex correspond to a colour in the respective urn and weights on the edges correspond to the number of balls of the respective colour. Increments happen based on atoms in independent homogeneous Poisson clocks with inhomogeneous intensities. For this highly interactive model, consider the case of sublinear reinforcement. After exploring a sensible notion of equilibrium distribution for these dynamics, this thesis shows sufficient conditions on the reinforcement rate so that the weights converge to the unique equilibrium distribution on infinite graphs of bounded degree.
Recommended citation: Y. Couzinié. “Sublinearly reinforced Pólya urns on graphs of bounded degree”. Master’s thesis, Ludwig Maximilian University of Munich, 2018.
BibTeX (also as a download):
@mastersthesis{couzinieMaster,
author = "Yannick Couzini\'{e}",
title = "Sublinearly reinforced Pólya urns on graphs of bounded degree",
school = "Ludwig Maximilian University of Munich",
year = "2018",
address = "Munich, Germany",
month = sep
}