8 papers · 1 filter
Renormalisation of Inhomogeneous Random Graphs
Luca Avena, Diego Garlaschelli, Rajat Subhra Hazra +1
We consider inhomogeneous random graphs in which vertices are assigned i.i.d.\ random weights, pairs of distinct vertices are connected by an edge independently with a probability…
Counterintuitive problems in discrete probability
Luca Avena, Gianmarco Bet, Bernardo Busoni
This manuscript contains a collection of counterintuitive problems in discrete probability, together with detailed solutions. The dataset was constructed as part of a broader resea…
node2vec or triangle-biased random walks: stationarity, regularity & recurrence
Luca Avena, Gianmarco Bet, Lars Schroeder +1
The node2vec random walk is a non-Markovian random walk on the vertex set of a graph, widely used for network embedding and exploration. This random walk model is defined in terms…
Semicircle laws with combined variance for non-uniform ErdÅs-Rényi hypergraphs
Luca Avena, Elia Bisi, Eleonora Bordiga
We consider ErdÅs-Rényi-type random hypergraphs that are non-uniform, in the sense that hyperedges of different sizes may coexist, and inhomogeneous, in that connection probabili…
A cohesive account on the ergodic behaviours and scaling limits of Random Walks in Cooling Random Environments
Luca Avena, Conrado da Costa
Transport in disordered media is a central theme in probability and statistical physics, where randomness in the underlying medium produces phenomena such as localization, anomalou…
Voter model on heterogeneous directed networks
Luca Avena, Federico Capannoli, Diego Garlaschelli +1
We investigate the consensus dynamics of the voter model on large random graphs with heterogeneous and directed features, focusing in particular on networks with power-law degree d…