SPTRF (277004)

  https://cordis.europa.eu/project/id/277004

  FP7 (2007-2013)

  Studies in Probability Theory and Related Fields

  Marie Curie Action: "Reintegration Grants" (FP7-PEOPLE-2009-RG)

  computer and information sciences  ·  combinatorics  ·  statistics and probability

  2011-05-01 Start Date (YY-MM-DD)

  2015-10-31 End Date (YY-MM-DD)

  € 100,000 Total Cost

  Description

The proposed project combines several studies in Probability Theory and its connections with Statistical Physics, Computer Science, Combinatorics and Approximation Theory. The first two studies aim to uncover the Gibbs-state structure of two statistical physics models in high dimensions - the anti-ferromagnetic 3-state Potts model and the hard-core model. These studies are intimately related to combinatorial questions of the rigidity of independent sets and proper 3-colorings in the high-dimensional cubic lattice. The third study aims to investigate the notion of independence sensitivity of a boolean function, a notion coming from computer science and error-correcting codes, in the context of complex statistical physics functions such as the percolation crossing function. In the fourth study we will investigate the existence and geometric properties of optimal allocations of mass in an infinite volume setting. This study continues recent developments on factor-map extensions of spatial processes. In the final study, we aim to use probabilistic and analytic tools to answer a long-standing question in approximation theory: how well can Lebesgue measure on the sphere be approximated by a prescribed number of point masses? These studies will significantly extend our understanding of probability theory and its related fields.

  Complicit Organisations

1 Israeli organisation participates in SPTRF.