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Variational formulas, Busemann functions, and fluctuation exponents for the corner growth model with exponential weights - Lecture 1

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Post-edited
Authors : Seppäläinen, Timo (Author of the conference)
CIRM (Publisher )

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limiting shape functions tilt-velocity duality stationary cocycles ergodic theorem for cocycles point-to-level variational formula point-to-point variational formula cocycles adapted to the potential Busemann functions stationary percolation questions of the audience
Abstract : Variational formulas for limit shapes of directed last-passage percolation models. Connections of minimizing cocycles of the variational formulas to geodesics, Busemann functions, and stationary percolation.

MSC Codes :
60K35 - Interacting random processes; statistical mechanics type models; percolation theory
 60K37 - Processes in random environments
 82C22 - Interacting particle systems
 82C43 - Time-dependent percolation
 82D60 - Polymers (statistical mechanics)
Additional resources :
http://www.cirm-math.fr/ProgWeebly/Renc1559/Seppalainen.pdf
    Information on the Video

    Film maker : Hennenfent, Guillaume
    Language : English
    Available date : 16/03/17
    Conference Date : 06/03/17
    Subseries : Research School
    arXiv category : Probability
    Mathematical Area(s) : Probability & Statistics ; Mathematical Physics
    Format : MP4 (.mp4) - HD
    Video Time : 01:31:47
    Targeted Audience : Researchers ; Graduate Students
    Download : https://videos.cirm-math.fr/2017-03-06_Seppalainen_Part1.mp4
Information on the Event

Event Title : Jean-Morlet Chair - Doctoral school: Random structures in statistical mechanics and mathematical physics / Chaire Jean-Morlet - Ecole doctorale : Structures aléatoires en mécanique statistique et physique mathématique
Event Organizers : Khanin, Konstantin ; Seppäläinen, Timo ; Shlosman, Senya
Dates : 06/03/17 - 10/03/17
Event Year : 2017
Event URL : https://www.chairejeanmorlet.com/1559.html

Citation Data

DOI : 10.24350/CIRM.V.19138103
Cite this video as: Seppäläinen, Timo (2017). Variational formulas, Busemann functions, and fluctuation exponents for the corner growth model with exponential weights - Lecture 1. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19138103
URI : http://dx.doi.org/10.24350/CIRM.V.19138103

See Also

Bibliography

  • Balázs, M., Cator, E., & Seppäläinen, T. (2006). Cube root fluctuations for the corner growth model associated to the exclusion process. Electronic Journal of Probability, 11(42), 1094–1132 - https://arxiv.org/abs/math/0603306

  • Balázs, M., & Seppäläinen, T. (2010). Order of current variance and diffusivity in the asymmetric simple exclusion process. Annals of Mathematics. Second Series, 171(2), 1237–1265 - http://dx.doi.org/10.4007/annals.2010.171.1237

  • Georgiou, N., Rassoul-Agha, F., Seppäläinen, T., & Yilmaz, A. (2015). Ratios of partition functions for the log-gamma polymer. The Annals of Probability, 43(5), 2282–2331 - http://projecteuclid.org/euclid.aop/1441792286

  • Georgiou, N., Rassoul-Agha, F., & Seppäläinen, T. (2016). Variational formulas and cocycle solutions for directed polymer and percolation models. Communications in Mathematical Physics, 346(2), 741–779 - http://dx.doi.org/10.1007/s00220-016-2613-z

  • Rassoul-Agha, F., Seppäläinen, T., & Yilmaz, A. (2013). Quenched free energy and large deviations for random walks in random potentials. Communications on Pure and Applied Mathematics, 66(2), 202–244 - http://dx.doi.org/10.1002/cpa.21417

  • Rassoul-Agha, F., & Seppäläinen, T. (2014). Quenched point-to-point free energy for random walks in random potentials. Probability Theory and Related Fields, 158(3-4), 711–750 - http://dx.doi.org/10.1007/s00440-013-0494-z


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