Wykaz obszarów badawczych związanych z tagiem Probabilistyka:
| # | Obszar badawczy | Dziedzina naukowa |
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| 1 |
My area of expertise is probability theory.
Strand 1. Applications of probabilistic, algebraic and analytic methods in modern mathematical statistics, especially in graphical models. In particular, I study the problem of model selection for so-called colored graphical models.
Strand 2. The study of distributions of solutions of stochastic fixed point equations (equivalently - iterated random functions or systems). I am particularly interested in generalizations of known problems to the case of infinite matrices and relations to free probability.
Strand 3. Characterizations of probability distributions (of the type of the Kac-Bernstein Theorem), the Rosenblatt transformation and their relations with ""integrable probability"", directed polymers and in general with the KPZ universality class.
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| 2 |
My research focuses on probability theory and its noncommutative generalization - the so-called free probability.
Noncommutative probability naturally arises when considering large independent random matrices, hence my interest in random matrix theory. Large random matrices in the limit converge to certain bounded operators on a Hilbert space. At the same time, elegant combinatorial structures such as lattices of non-crossing or interval partitions are used to describe free probability. On the other hand, analytic functions are used to describe the distribution. In summary, noncommutative probability uses a wide range of mathematical tools and interesting questions will be found in it for those interested in probability theory, combinatorics, functional analysis or complex analysis.
My research focuses on combinatorial aspects and connections with random matrices.
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