Servet Martínez

Research Area:
Probability and Ergodic Theory

Works at:
CMM Climate & Biodiversity • CMM Digital Health • Mathomics

Research interests:
My research focuses on Markov chains, discrete potential theory, dynamical systems and stochastic modeling. In the last twenty years I have worked on killed processes and quasi-stationary distributions (q.s.d.), in particular we have supply the best result up to now on the existence of q.s.d. for countable infinite Markov chains, we have classified completely the killed diffusions and killed birth and death chains, we have interpreted the Gibbs state of dynamical systems via q.s.d.

On discrete potential theory we have introduced the ultrametric matrices showing that they are potential matrices and extend it to a infinite matrices and to a continuous framework. For algebraic cellular automata and symbolic dynamics we have studied the convergence to equilibrium and the rigidity of its invariant distributions.
In stochastic modeling we have studied the oresize distribution of rocks resulting from mining processes and using fragmentation theory to study the fragmentation energy involved in these processes (Bertoin, Devoto).