Christophe Garban is a mathematician whose research connects probability theory with statistical physics. His institutional and personal pages identify work on percolation, phase transitions and scaling limits, with a professorship at Lyon 1 beginning in 2014.[ref]
His work with collaborators constructs limiting measures for pivotal sites, clusters and interfaces in critical planar percolation. A pivotal site is a location whose state can change a macroscopic connectivity event. Counting such locations requires a scale-dependent normalization before a nontrivial continuum limit emerges. The resulting measures make sensitivity to microscopic changes part of the limiting geometry.[ref]
Pivotal, cluster and interface measures for critical planar percolation by Christophe Garban and others. Abstract and Introduction: pivotal measures, conformal covariance and cluster/interface measures
With Nathanaël Berestycki and Arnab Sen, he also constructed a state-space description yielding convergence from coalescing random walks to a coalescing Brownian flow with only finite variance of the increments. This connects his study of continuum random geometry with interacting stochastic paths.[ref]
Coalescing Brownian flows: A new approach by Nathanaël Berestycki and others. Abstract: finite-variance invariance principle and topology motivated by planar percolation
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