Research Seminar "Representations and Probability 2"
- Knowledge of key notions and results in asymptotic representations theory
- Knowledge of key notions and results in theory of random point fields, including determinantal processes.
- Knowledge of key results in theory of determinantal processes. Ability to use them to study properties of simple DPs.
- Knowledge of key results and methods in asymptotic representations theory, including asymptotic theory of characters.
- Knowledge of main results in theory of othogonal polynomials (Christoffel-Darboux kernels, etc.) Familiarity with asymtotic results for orthogonal polynomial ensembles.
- Orthogonal polynomials and random point processesElements of theory of orthogonal polynomial ensembles. Their relations to random point processes. Asymptotic problems for point processes and the corresponding functional-analytic properties of the assocuated orthogonal polynomial ensembles.
- Determinantal processesDefinition. Correlation functions. Kernel of a process and the associated operator in L2. Macchi-Soshnikov theorem. Properties of DP: rigidity, behaviour of conditional measures.
- Asymptotic representations theoryKey problems in ART. Invariant measures on spaces of matrices. Spectres distributions and their asymptotics.
- Fulton, W. (1997). Young Tableaux : With Applications to Representation Theory and Geometry. Cambridge [England]: Cambridge University Press. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=570403
- Fuad Aleskerov, & Andrey Subochev. (2013). Modeling optimal social choice: matrix-vector representation of various solution concepts based on majority rule. Journal of Global Optimization, (2), 737. https://doi.org/10.1007/s10898-012-9907-2