Stable random fields


A mini course to be given in The third Indo-Russian meeting in probability and statistics

Rough plan:
  • Day 1 (Jan 08, 2018): Symmetric stable distribution, random measure and integral representation.
  • Day 2 (Jan 09, 2018)Nonsingular group action, Hopf decomposition and Rosinski representation.
  • Day 3 (Jan 10, 2018): All play and no work makes us dull probabilists :-).
  • Day 4 (Jan 11, 2018): Left-stationary symmetric stable random fields indexed by a lattice and by a finitely generated free group.
  • Day 5 (Jan 12, 2018): Connections to von Neumann algebras and discussion of open problems. 

Resources:
 
For Day 1 - Day 4 ("lattice" part)R. (2017)Maxima of stable random fields, nonsingular actions and finitely generated abelian groups: A surveyIndian Journal of Pure and Applied Mathematics 48(4): 513-540. Dedicated to Professor B. V. Rao.
 
For Day 4 (''free group" part): (1) Sarkar and R. (2016)Stable random fields indexed by finitely generated free groupsTo appear in Annals of ProbabilityBased on Sourav Sarkar's master's dissertation at Indian Statistical Institute. (2) Slides of a talk on this work. 
 
For Day 5: (1) References for basics of von Neumann algebras can be found here. (2) Slides on this work. (3) The paper will be arXived and linked here in near future (hopefully :-)). (4) For open problems, see Section 8.1 of R. (2017) and Section 4.5 of Sarkar and R. (2016). (5) More open problems will be discussed towards the end. 
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