Name: Paolo Dai Pra
Date and place of birth: november 1, 1962, Venezia.
Affiliation: Dipartimento di Matematica Pura e Applicata, Università degli Studi di Padova, Via Trieste 63, 35121 Padova. E-mail: daipra@math.unipd.it
Web page: www.math.unipd.it/~daipra
Studies: “Laurea” in Mathematics, University of Padua, 1986, 110/110 cum laude. • Ph.D. in Mathematics, Rutgers University, under the direction of Prof. J.L. Lebowitz, 1992.
Academic career: 1992-1998: Assistant Professor, Department of Mathematics, University of Padua. • 1998-2000 : Associate Professor, Department of Mathematics, Milan Polytechnical Institute. • 2000- : Full professor, Department of Mathematics, University of Padua.
Research interests.
1. Complex systems in Biological and social sciences.
This tops refers to the collective behavior of Markovian dynamics with many degrees of freedom, motivated by various applications. One example is the study of multicellular systems and neuronal networks, where collective synchronization phenomena emerge, i.e. periodic behavior at macroscopic level, even in absence of applied periodic forces. Another example is given by models of contagion in Economics, where interactions between “agents” may produce systemic risk.
Paolo Dai Pra, Markus Fischer, Daniele Regoli (2013). A Curie-Weiss Model with Dissipation. JOURNAL OF STATISTICAL PHYSICS, vol. 152, p. 37-53
Paolo Dai Pra, Elena Sartori, Marco Tolotti (2013). Strategic Interaction in Trend-Driven Dynamics. JOURNAL OF STATISTICAL PHYSICS, vol. 152, p. 724-741
DAI PRA P, RUNGGALDIER W. J, SARTORI E., TOLOTTI M (2009). Large portfolio losses: A dynamic contagion model . THE ANNALS OF APPLIED PROBABILITY, vol. 19, p. 347-394
2. Geometric and scaling properties of stochastic processes.
Stochastic processes with jumps, in particular on discrete structures, have interesting properties of geometric-combinatorial nature. Problems studied include the classification of jump processes in terms of their reciprocal properties, monotone realization of continuous-time Markov processes, the analysis of scaling properties of financial data, with the proposal of stylized models fitting these data.
G. Conforti, P. Dai Pra, S. Roelly, Reciprocal class of jump processes, June 2014, submitted for publication.
P. DAI PRA, P.Y. Louis, I. G. Minelli (2010). Realizable monotonicity for continuous-time Markov processes. STOCHASTIC PROCESSES AND THEIR APPLICATIONS, vol. 120, p. 959-982
ALESSANDRO ANDREOLI, FRANCESCO CARAVENNA, PAOLO DAI PRA, GUSTAVO POSTA (2012). Scaling and multiscaling in financial series: a simple model. ADVANCES IN APPLIED PROBABILITY, vol. 44, p. 1018-1051
3. Convergence to equilibrium and functional inequalities for interacting particle systems.
The topic is concerned with quantitative estimates on the rate of convergence to equilibrium of Markovian dynamics. One important tool to obtain this rate is provided by functional inequalities (Poincarè, logarithmic-Sobolev, Nash,...). Sharp estimates for the best constants in these inequalities allow in particular to obtain the dependence of the rate of convergence on the number of degrees of freedom. I have obtained various estimates on the Poincarè and logarithmic-Sobolev inequalities for Glauber and exchange dynamics. In particular we solved a conjecture concerning the diffusing scaling of the logarithmic-Sobolev constant for zero-range processes.
Paolo Dai Pra, Gustavo Posta (2013). Entropy decay for interacting systems via the Bochner-Bakry-Émery approach. ELECTRONIC JOURNAL OF PROBABILITY, vol. 18, p. 1-40
DAI PRA P., BOUDOU A.S., CAPUTO P., POSTA G. (2006). Spectral gap estimates for interacting particle systems via a Bochner-type identity. JOURNAL OF FUNCTIONAL ANALYSIS, vol. 232, p. 222-258
DAI PRA P., POSTA G. (2005). Logarithmic Sobolev inequality for zero range dynamics. ANNALS OF PROBABILITY, vol. 33, p. 2355-2401