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| Author(s): |
Victor Guerreiro Vendruscollo
Total Authors: 1
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| Document type: | Master's Dissertation |
| Press: | São Carlos. |
| Institution: | Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC/SB) |
| Defense date: | 2023-02-28 |
| Examining board members: |
Guilherme Lima Ferreira da Silva;
Daniel Ungaretti Borges;
Alexsandro Giacomo Grimbert Gallo;
Ana Paula Peron
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| Advisor: | Guilherme Lima Ferreira da Silva |
| Abstract | |
It may sound absurd to believe that a traffic jam model, eigenvalues of random matrices, and the length of the longest increasing subsequence of random permutations have a connection. Mathematicians say otherwise. Surprising results show that some fluctuations of these and many other models have the same asymptotic behavior. The development of integrable probability, a branch of representation theory applied to probability, is crucial for such findings. The totally asymmetric simple exclusion process (TASEP) is an interacting particle system that simulates traffic. We find the TASEP in a particular parametrization of a more general object, the Schur process, which is the main object of this study. (AU) | |
| FAPESP's process: | 20/16783-8 - Random particle systems and Schur processes |
| Grantee: | Victor Guerreiro Vendruscollo |
| Support Opportunities: | Scholarships in Brazil - Master |