Nina Javerzat

Rigidity Percolation (RP) attracted the attention of soft matter physicists, as an elegant framework to understand the emergence of solidity in media that not present any long-range structural order. The solidification of amorphous systems like gels, fiber networks or living tissues can indeed be understood by focusing on locally rigid structures -- clusters, that form and grow until one eventually percolates the whole system, giving it macroscopic mechanical stability.
Rigidity Percolation can be defined rigorously from the concept of graph rigidity, and I will give an overview of some mathematical results. I will explain how the unique non-local character of RP makes it fundamentally different from the usual Connectivity Percolation (CP) problem, and summarize the state of the art in the physics literature, about the RP transition and its universality class.
I will then present my own contributions, about the conformal invariance of RP. I will explain a first work where I gave (non rigorous!) numerical evidence of conformal invariance from properties of the connectivity functions -- the probabilities that points belong to the same rigid clusters, and present a subsequent work where I found numerical evidence that the interfaces of rigid clusters are consistent with Schramm-Loewner Evolution processes. This allows notably to obtain a new relation between two of the critical exponents of RP.
A lot remains to be understood about Rigidity Percolation, and I will end with my favourite perspectives.