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This workshop will be about percolation and fist passage percolation models, with a focus on pivotality/gradient tools, which are key tools when one studies phase transitions or the sensitivity of the model to perturbations.

• Anna Donadini: Noise sensitivity and directed polymers (joint work with Francesco Caravenna)
• Loïc Gassmann: Generic arm separation for planar percolation (joint work with Ioan Manolescu and Maran Mohanarangan)
• Régine Marchand: The contact process can survive on a slightly subcritical dynamical percolation cluster (joint work with Aurelia Deshayes)

The workshop will take place from Monday, March 30 (11 am) to Wednesday, April 1 (noon) at Institut Fourier in "salle de lecture B29" (this room is very close to the entrance of the building, just on the right of the library).

How to go to Institut Fourier: From Grenoble main station, take Tram B (towards Gières) and get off at "Bibliothèques Universitaires" (this will take between 20 and 25 minutes). Then walk during 1 minute: the lab is just behind the restaurant "Le Martin's".

Organised by Barbara Dembin, Hugo Vanneuville and Institut Fourier. If you have any question, please send an email to hugo.vanneuville [at] univ-grenoble-alpes [dot] fr .

Monday 30rd: 

• 10am - 11am: Welcome
  
• 11am - 12:15am: Barbara Dembin 1
• 12:15am - 2pm: Buffet
• 2pm - 3:15pm: Franco Severo 1
• 3:15pm - 4pm: Coffee break
• 4pm -5pm: Anna Donadini

Tuesday 31st: 

• 9am - 10:15am: Hugo Vanneuville 1
• 10:15am - 11am: Coffee break
• 11am - 12:15am: Barbara Dembin 2
• 12:15am - 2pm: Buffet
• 2pm - 3pm: Régine Marchand
• 3:45pm - 5pm: Franco Severo 2

Wednesday 1st:

•  8:45am - 9:45: Loïc Gassmann
• 9:45am - 10:30am: Coffee break
• 10:30am - 11:45am: Hugo Vanneuville 2
• 12am - 1:30pm: Buffet

Anna Donadini: Noise sensitivity and directed polymers (joint work with Francesco Caravenna) Noise sensitivity for functionals of independent random variables, introduced by Benjamini, Kalai and Schramm in 1999 in the context of Boolean functions, describes the phenomenon where a small perturbation of the underlying randomness leads to an asymptotically independent outcome.

In this talk, we extend classical noise sensitivity criteria beyond the Boolean setting and derive quantitative estimates with optimal rates. We then consider the model of directed polymers in random environments, and apply our results to the regime in which the partition function converges to a universal limit known as the Stochastic Heat Flow, which we show to be independent of the white noise arising from the scaling limit of the disorder.

Loïc Gassmann: Generic arm separation for planar percolation (joint work with Ioan Manolescu and Maran Mohanarangan) Arm separation is an essential tool in critical planar percolation with numerous applications. It essentially states that when a collection of connections goes from the center of a large box to its boundary, then near the boundary these connections are typically far apart. 
In this talk, we present a new proof of this result that does not follow the classical multi-scale approach of Kesten, but instead uses an exploration procedure. Our result relies on a generic exploration argument that allows to "separate" arms in any planar percolation (without assuming RSW nor FKG). Since our proof uses only a single-scale argument, our separation result is robust enough to allow all sorts of conditioning at macroscopic distance from the boundary.