Dr. Angelica Pachon has recently published two papers. The first, entitled "On the continuous time limit of the Barabasi-Albert random graph" has been accepted for publication in the Journal “Applied Mathematics and Computation” . The paper is joint work with Federico Polito and Laura Sacerdote of the Department of Mathematics at University of Turin, Italy. They prove that the Barabási-Albert model converges weakly to a set of generalized Yule models via an appropriate scaling. To pursue this aim they superimpose to its graph structure a suitable set of processes that they call the planted model and they introduce an ad-hoc sampling procedure. The use of the obtained limit process represents an alternative and advantageous way of looking at some of the asymptotic properties of the Barabási-Albert random graph. https://doi.org/10.1016/j.amc.2020.125177

The second, entitled "On Discrete time semi Markov processes" accepted for publication in the Journal “Discrete and Continuos Dynamical Systems Series B” . The paper is joint work with Federico Polito and Constantino Ricciuti of the Department of Mathematics at University of Turin, Italy. In the last years, many authors studied a class of continuous time semi-Markov processes obtained by time-changing Markov processes by hitting times of independent subordinators. Such processes are governed by integro-differential convolution equations of generalized fractional type. The aim of this paper is to develop the discrete-time version of such a theory. They show that a class of discrete-time semi-Markov chains can be seen as time-changed Markov chains and they obtain governing convolution type equations. Such processes converge weakly to those in continuous time under suitable scaling limits. http://dx.doi.org/10.3934/dcdsb.2020170