By S. V. Kerov
This publication reproduces the doctoral thesis written by means of a extraordinary mathematician, Sergei V. Kerov. His premature loss of life at age fifty four left the mathematical neighborhood with an in depth physique of labor and this extraordinary monograph. In it, he provides a transparent and lucid account of effects and strategies of asymptotic illustration conception. The ebook is a different resource of knowledge at the very important subject of present learn. Asymptotic illustration idea of symmetric teams bargains with difficulties of 2 varieties: asymptotic homes of representations of symmetric teams of huge order and representations of the restricting item, i.e., the endless symmetric team. the writer contributed considerably within the improvement of either instructions. His publication provides an account of those contributions, in addition to these of alternative researchers. one of the difficulties of the 1st kind, the writer discusses the homes of the distribution of the normalized cycle size in a random permutation and the restricting form of a random (with admire to the Plancherel degree) younger diagram. He additionally experiences stochastic houses of the deviations of random diagrams from the restricting curve. one of the difficulties of the second one variety, Kerov experiences a massive challenge of computing irreducible characters of the endless symmetric staff. This results in the research of a continuing analog of the suggestion of younger diagram, and specifically, to a continual analogue of the hook stroll set of rules, that is renowned within the combinatorics of finite younger diagrams. In flip, this building presents a totally new description of the relation among the classical second difficulties of Hausdorff and Markov. The publication is appropriate for graduate scholars and examine mathematicians drawn to illustration thought and combinatorics.
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