Azioni sul documento
Seminario: The law of series
| Cosa | |
|---|---|
| Quando |
05/03/2007 15:00
05/03/2007 18:00
05/03/2007 da 15:00 al 18:00 |
| Dove | Sala riunioni |
| Persona di riferimento | Giovanni Panti |
| Indirizzo e-mail per contatti | giovanni.panti@dimi.uniud.it |
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Il prof. Yves Lacroix, dell'Universita' di Tolone, terra' un seminario dal titolo The law of series.
Abstract. The simplest model of a dynamical system in the probabilistic setting is the one obtained by a stationary ergodic process. For such process, Kolmogorov introduced the notion of entropy, which connects to the one discussed by Shannon when he was working at the Bell laboratories. The entropy is just a positive real number, and it is non zero if and only if the system is non invertible, that is the present does not only depend on the past. In other words, the system is non deterministic.
Any system can be pictured in the probabilistic sense by simple procedures, which are connected to quantification of recurrence to some events. Asymptotically, many processes admit a behaviour which is much like the one of the independent process. So I have tried to understand possible asymptotics, in order to go beyond the independent or independent-like cases. After obtaining some characterizations, with T. Downarowicz, we have succeeded in proving that non determinism has an unexpected consequence : asymptotics can only reveal clustering of rare events, which means that positivity of this simple object, entropy, implies that no matter what one tries, rare events will have a natural tendency to cluster... like in the popular but yet unmodelled "law of series".
We have even proved that a typical partition of a positive entropy system produces a process with extreme clustering on an upper density one sequence of cylinder lengths. I will try to make this story comprehensive during my talk.
Tutti gli interessati sono cordialmente invitati.
Abstract. The simplest model of a dynamical system in the probabilistic setting is the one obtained by a stationary ergodic process. For such process, Kolmogorov introduced the notion of entropy, which connects to the one discussed by Shannon when he was working at the Bell laboratories. The entropy is just a positive real number, and it is non zero if and only if the system is non invertible, that is the present does not only depend on the past. In other words, the system is non deterministic.
Any system can be pictured in the probabilistic sense by simple procedures, which are connected to quantification of recurrence to some events. Asymptotically, many processes admit a behaviour which is much like the one of the independent process. So I have tried to understand possible asymptotics, in order to go beyond the independent or independent-like cases. After obtaining some characterizations, with T. Downarowicz, we have succeeded in proving that non determinism has an unexpected consequence : asymptotics can only reveal clustering of rare events, which means that positivity of this simple object, entropy, implies that no matter what one tries, rare events will have a natural tendency to cluster... like in the popular but yet unmodelled "law of series".
We have even proved that a typical partition of a positive entropy system produces a process with extreme clustering on an upper density one sequence of cylinder lengths. I will try to make this story comprehensive during my talk.
Tutti gli interessati sono cordialmente invitati.
