22 citations · 103 across the 32 of their papers we have counts for
36 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 Erdős-Rényi hypergraphs
Luca Avena, Elia Bisi, Eleonora Bordiga
We consider Erdős-Rényi-type random hypergraphs that are non-uniform, in the sense that hyperedges of different sizes may coexist, and inhomogeneous, in that connection probabiliti…
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…
The voter model on random regular graphs with random rewiring
Luca Avena, Rangel Baldasso, Rajat Subhra Hazra +2
We consider the voter model with binary opinions on a random regular graph with vertices of degree , subject to a rewiring dynamics in which pairs of edges are rewire…
Mixing of fast random walks on dynamic random permutations
Luca Avena, Remco van der Hofstad, Frank den Hollander +1
We analyse the mixing profile of a random walk on a dynamic random permutation, focusing on the regime where the walk evolves much faster than the permutation. Two types of dynamic…
Limiting Spectra of inhomogeneous random graphs
Luca Avena, Rajat Subhra Hazra, Nandan Malhotra
We consider sparse inhomogeneous Erdős-Rényi random graph ensembles where edges are connected independently with probability . We assume that $p_{ij}= \varepsilon_N f(w_i,…
Meeting, coalescence and consensus time on random directed graphs
Luca Avena, Federico Capannoli, Rajat Subhra Hazra +1
We consider Markovian dynamics on a typical realization of the so-called Directed Configuration Model (DCM), that is, a random directed graph with prescribed in- and out-degrees. I…
Inhomogeneous random graphs with infinite-mean fitness variables
Luca Avena, Diego Garlaschelli, Rajat Subhra Hazra +1
We consider an inhomogeneous Erdős-Rényi random graph ensemble with exponentially decaying random disconnection probabilities determined by an i.i.d. field of variables with heavy…
Discordant edges for the voter model on regular random graphs
Luca Avena, Rangel Baldasso, Rajat Subhra Hazra +2
We consider the two-opinion voter model on a regular random graph with n vertices and degree . It is known that consensus is reached on time scale n and that on this time…
Gaussian, stable, tempered stable and mixed limit laws for random walks in cooling random environments
Luca Avena, Conrado da Costa, Jonathon Peterson
Random Walks in Cooling Random Environments (RWCRE) is a model of random walks in dynamic random environments where the entire environment is resampled along a fixed sequence of ti…
Loop-erased partitioning of a network: monotonicities & analysis of cycle-free graphs
Luca Avena, Jannetje Driessen, Twan Koperberg
We consider random partitions of the vertex set of a given finite graph that can be sampled by means of loop-erased random walks stopped at a random exponential time of parameter $…
Linking the mixing times of random walks on static and dynamic random graphs
Luca Avena, Hakan Güldaş, Remco van der Hofstad +2
This paper considers non-backtracking random walks on random graphs generated according to the configuration model. The quantity of interest is the scaling of the mixing time of th…
Laws of large numbers for weighted sums of independent random variables: a game of mass
Luca Avena, Conrado da Costa
We consider weighted sums of independent random variables regulated by an increment sequence. We provide operative conditions that ensure strong law of large numbers for such sums…
Loop-erased partitioning of a graph: mean-field analysis
Luca Avena, Alexandre Gaudilliere, Paolo Milanesi +1
We consider a random partition of the vertex set of an arbitrary graph that can be sampled using loop-erased random walks stopped at a random independent exponential time of parame…
Random walk in cooling random environment: recurrence versus transience and mixed fluctuations
Luca Avena, Yuki Chino, Conrado da Costa +1
This is the third in a series of papers in which we consider one-dimensional Random Walk in Cooling Random Environment (RWCRE). The latter is obtained by starting from one-dimensio…
Random walks on dynamic configuration models: a trichotomy
Luca Avena, Hakan Guldas, Remco van der Hofstad +1
We consider a dynamic random graph on vertices that is obtained by starting from a random graph generated according to the configuration model with a prescribed degree sequence…
Random walk in cooling random environment: ergodic limits and concentration inequalities
L. Avena, Y. Chino, C. da Costa +1
In previous work by Avena and den Hollander, a model of a one-dimensional random walk in a dynamic random environment was proposed where the random environment is resampled from a…
Random Forests and Networks Analysis
L. Avena, F. Castell, A. Gaudilliere +1
D. Wilson~\cite{[Wi]} in the 1990's described a simple and efficient algorithm based on loop-erased random walks to sample uniform spanning trees and more generally weighted trees…
Approximate and exact solutions of intertwining equations through random spanning forests
Luca Avena, Fabienne Castell, Alexandre Gaudillière +1
For different reversible Markov kernels on finite state spaces, we look for families of probability measures for which the time evolution almost remains in their convex hull. Motiv…
The parabolic Anderson model on the hypercube
Luca Avena, Onur Gün, Marion Hesse
We consider the parabolic Anderson model on the -dimensional hypercube with random i.i.d. potential . We…
Random walks in cooling random environments
L. Avena, F. den Hollander
We propose a model of a one-dimensional random walk in dynamic random environment that interpolates between two classical settings: (I) the random environment is sampled at time ze…