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UID:6084@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20220412T143000
DTEND;TZID=Europe/Paris:20220412T153000
DTSTAMP:20241120T200909Z
URL:https://www.i2m.univ-amu.fr/evenements/rapid-mixing-of-gibbs-samplers-
 coupling-spectral-independence-and-entropy-factorizations/
SUMMARY:Pietro Caputo (Roma 3): Rapid mixing of Gibbs samplers: Coupling\,
  Spectral Independence\, and Entropy factorizations.
DESCRIPTION:Pietro Caputo: \n\nWe discuss some recent developments in the a
 nalysis of convergence to stationarity for the Gibbs sampler of general sp
 in systems on arbitrary graphs. These are based on two recently introduced
  concepts: Spectral Independence and Block Factorization of Entropy. We sh
 ow that if a system is spectrally independent then its entropy functional 
 satisfies a general block factorization\, which in turn implies a modified
  log-Sobolev inequality and a tight control of the mixing time for the Gla
 uber dynamics as well as for any other heat bath block dynamics. Moreover\
 , we show that the existence of a contractive coupling for a local Markov 
 chain implies that the system is spectrally independent. As a corollary\, 
 we obtain new optimal bounds on the mixing time of a large class of sampli
 ng algorithms for the ferromagnetic Ising/Potts models in the so-called tr
 ee-uniqueness regime\, including non-local Markov chains such as the Swend
 sen-Wang dynamics. The methods also apply to spin systems with hard constr
 aints such as q-colorings of a graph and the hard-core gas. Based on some 
 recent joint works with Antonio Blanca\, Zongchen Chen\, Daniel Parisi\, A
 listair Sinclair\, Daniel Stefankovic\, and Eric Vigoda.\n\n[su_spacer]
ATTACH;FMTTYPE=image/jpeg:https://www.i2m.univ-amu.fr/wp-content/uploads/2
 022/04/Pietro_Caputo.jpg
CATEGORIES:Séminaire,Probabilités
LOCATION:I2M Chateau-Gombert - CMI\, Salle de Séminaire R164 (1er étage)\
 , 39 Rue Joliot Curie\, 13013 Marseille\, France\, Campus Château-Gombert
 \, 
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