PhD Defense Lorenzo Federico
Lorenzo Federico will defend his PhD thesis entitled 'Phase transitions and connectivity in random graphs' on March 9th, 2020.
Lorenzo's promotors are Remco van der Hofstad and Frank den Hollander.
The PhD defense will start at 11:00 hrs and will take place in room 0.710 of the Atlas Building of Eindhoven University of Technology.
Lorenzo is working as a research assistant with Agelos Georgakopoulos at Warwick University, focusing his research on random minimal spanning structures and sequences of graph samled from graphons.
In this thesis, we present four different results about the phase transition in different random graph models for the existence of a giant component and for connectivity. We show how in the Configuration Model the asymptotic probability of connectivity is determined by the density of vertices of degree 1 and 2 and by the average degree of the graph. Moreover, when the limit connectivity probability is non-trivial, the graph minus the giant component is made of a Poisson-distributed number of components shaped like lines and cycles. We also study Hamming graph percolation, proving that connectivity is determined with high probability by the absence of isolated points and getting a more precise expansion of the critical point for the existence of a giant component in terms of inverse powers of the degree. Finally, we compute the scaling limit for the number of vertices and edges in the largest component of a critical Random Intersection Graph, showing that the critical exponent depends on the relative scaling between the numbers of individuals and communities.