3 papers
math.PR2019
The Directed Edge Reinforced Random Walk: The Ant Mill Phenomenon
Dirk Erhard, Tertuliano Franco, Guilherme Reis
We define here a \textit{directed edge reinforced random walk} on a connected locally finite graph. As the name suggests, this walk keeps track of its past, and gives a bias toward…
math.PR2018
Interacting diffusions on sparse graphs: hydrodynamics from local weak limits
Roberto I. Oliveira, Guilherme H. Reis, Lucas M. Stolerman
We prove limit theorems for systems of interacting diffusions on sparse graphs. For example, we deduce a hydrodynamic limit and the propagation of chaos property for the stochastic…
math.PR2018
Interacting diffusions on random graphs with diverging degrees: hydrodynamics and large deviations
Roberto I. Oliveira, Guilherme Reis
We consider systems of mean-field interacting diffusions, where the pairwise interaction structure is described by a sparse (and potentially inhomogeneous) random graph. Examples i…