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Post-edited Integrable probability - Lecture 1

Auteurs : Corwin, Ivan (Auteur de la Conférence)
CIRM (Editeur )

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$q$-TASEP Markov process generator step initial data Markov duality $q$-Boson process $q$-TASEP and $q$-boson duality true evolution equation $k$-particle space restriction free evolution equation with boundary conditions $q$-TASEP moment formula nested contour integral formula $e_q$-Laplace transform Fredholm determinant formula Tracy-Widom GUE asymptotics Kardar-Parisi-Zhang universality class O'Connell-Yor semi-discrete directed polymer Kardar-Parisi-Zhang equation

Résumé : A number of probabilistic systems which can be analyzed in great detail due to certain algebraic structures behind them. These systems include certain directed polymer models, random growth process, interacting particle systems and stochastic PDEs; their analysis yields information on certain universality classes, such as the Kardar-Parisi-Zhang; and these structures include Macdonald processes and quantum integrable systems. We will provide background on this growing area of research and delve into a few of the recent developments.

Kardar-Parisi-Zhang - interacting particle systems - random growth processes - directed polymers - Markov duality - quantum integrable systems - Bethe ansatz - asymmetric simple exclusion process - stochastic partial differential equations

Codes MSC :
60H15 - Stochastic partial differential equations
82B23 - Exactly solvable models; Bethe ansatz
82C22 - Interacting particle systems

Informations sur la rencontre

Nom du congrès : School on disordered systems, random spatial processes and some applications : introductory school / Ecole sur les systèmes désordonnés, processus spatiaux aléatoires et certaines applications : école d'introduction
Organisteurs Congrès : Bouchaud, Jean-Philippe ; Contucci, Pierluigi ; Giardina, Cristian ; Sidoravicius, Vlada ; Nolin, Pierre ; Vargas, Vincent
Dates : 05/01/15 - 09/01/15
Année de la rencontre : 2015
URL Congrès : http://random15.dm.unibo.it/s_introductory

Citation Data

DOI : 10.24350/CIRM.V.18660203
Cite this video as: Corwin, Ivan (2015). Integrable probability - Lecture 1. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.18660203
URI : http://dx.doi.org/10.24350/CIRM.V.18660203

Voir aussi

Bibliographie

  1. Borodin, A., Corwin, I., & Sasamoto, T. (2014). From duality to determinants for $q$-TASEP and ASEP. <arXiv:1207.5035> - http://arxiv.org/abs/1207.5035

  2. Borodin, A., Corwin, I., Petrov, L., & Sasamoto, T. (2014). Spectral theory for the $q$-Boson particle system. <arXiv:1308.3475> - http://arxiv.org/abs/1308.3475

  3. Borodin, A., Corwin, I., Petrov, L., & Sasamoto, T. (2014). Spectral theory for interacting particle systems solvable by coordinate Bethe ansatz. <arXiv:1407.8534> - http://arxiv.org/abs/1407.8534

  4. Corwin, I. (2014). EXACT Exact solvability of some SPDEs. MSRI Summer Graduate School on Stochastic Partial Differential Equations, Jul 2014, Berkeley, California, United States - http://www.math.columbia.edu/~corwin/MSRIJuly2014.pdf

  5. Corwin, I. (2014). Macdonald processes, quantum integrable systems and the Kardar-Parisi-Zhang universality class. <arXiv:1403.6877> - http://arxiv.org/abs/1403.6877

  6. Corwin, I. (2014). The $(q, \mu, \nu)$-Boson process and $(q, \mu, \nu)$-TASEP. <arXiv:1401.3321> - http://arxiv.org/abs/1401.3321



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