2 citations · 2 across the 8 of their papers we have counts for
9 papers · 1 filter
On the phase transition for the number of collisions on comb graphs
Umberto De Ambroggio, Jenson Ng, Maximilian Nitzschner +1
We consider collisions of simple random walks on comb graphs , which are obtained by attaching vertical segments of the form …
Very large cliques in a scale-free random graph
Carlo De Ambroggio, Umberto De Ambroggio
In this short article we consider a preferential attachment random graph model with edge steps, studied by Alves, Ribeiro and Sanchis. Starting with an initial graph …
Small maximal clusters are very unlikely in critical random graphs
Umberto De Ambroggio
We describe a probabilistic methodology, based on random walk estimates, to obtain exponential upper bounds for the probability of observing unusually small maximal components in t…
Limit Laws for Critical Dispersion on Complete Graphs
Umberto De Ambroggio, Tamás Makai, Konstantinos Panagiotou +1
We consider a synchronous process of particles moving on the vertices of a graph , introduced by Cooper, McDowell, Radzik, Rivera and Shiraga (2018). Initially, particles ar…
Dispersion on the Complete Graph
Umberto De Ambroggio, Tamás Makai, Konstantinos Panagiotou
We consider a synchronous process of particles moving on the vertices of a graph , introduced by Cooper, McDowell, Radzik, Rivera and Shiraga (2018). Initially, particles ar…
A simple path to component sizes in critical random graphs
Umberto De Ambroggio
We describe a robust methodology, based on the martingale argument of Nachmias and Peres and random walk estimates, to obtain simple upper and lower bounds on the size of a maximal…
The probability of unusually large components for critical percolation on random -regular graphs
Umberto De Ambroggio, Matthew I. Roberts
Let be a fixed integer, , and let be a positive integer such that is even. Let be a (random) graph on vertices obtaine…
An elementary approach to component sizes in critical random graphs
Umberto De Ambroggio
In this article we introduce a simple tool to derive polynomial upper bounds for the probability of observing unusually large maximal components in some models of random graphs whe…
Upper bounds for the largest components in critical inhomogeneous random graphs
Umberto De Ambroggio, Angelica Pachon
We consider the Norros-Reittu random graph , where edges are present independently but edge probabilities are moderated by vertex weights, and use probabilistic a…