Related papers: Max-convolution semigroups and extreme values in l…
Progress on the conjecture of Banica and Bichon that the classical permutation group is a maximal quantum subgroup of the quantum permutation group remains limited to a handful of small-parameter results. By Tannaka--Krein duality, any…
Based on a new analytical approach to the definition of additive free convolution on probability measures on the real line we prove free analogs of limit theorems for sums for non-identically distributed random variables in classical…
In this paper additive bi-free convolution is defined for general Borel probability measures, and the limiting distributions for sums of bi-free pairs of selfadjoint commuting random variables in an infinitesimal triangular array are…
We determine the distributional behavior for products of free random variables in a general infinitesimal triangular array. In the case of positive variables, the main theorem extends a result proved earlier for arrays with identically…
In this thesis we study convolutions that arise from noncommutative probability theory. We prove several regularity results for free convolutions, and for measures in partially defined one-parameter free convolution semigroups. We discuss…
We present an algorithm to explore various properties of the numerical semigroups with a given maximum primitive. In particular, we count the number of such numerical semigroups and verify that there is no counterexample to Wilf's…
We find necessary and sufficient conditions on an (inverse) semigroup $X$ under which its semigroups of maximal linked systems $\lambda(X)$, filters $\phi(X)$, linked upfamilies $N_2(X)$, and upfamilies $\upsilon(X)$ are inverse.
We extend the notions of finite free convolution and finite free cumulants to the setting of formal power series by introducing their natural analogues, namely $t$-deformed convolution and $t$-deformed cumulants. In this framework, we…
In classical probability the law of large numbers for the multiplicative convolution follows directly from the law for the additive convolution. In free probability this is not the case. The free additive law was proved by D. Voiculescu in…
Recently, in a work that grew out of their exploration of interlacing polynomials, Marcus, Spielman and Srivastava and then Marcus studied certain combinatorial polynomial convolutions. These convolutions preserve real-rootedness and…
We use the description of the Schutzenberger automata for amalgams of finite inverse semigroups given by Cherubini, Meakin, Piochi to obtain structural results for such amalgams. Schutzenberger automata, in the case of amalgams of finite…
In a 1999 paper, Bercovici and Pata showed that a natural bijection between the classically, free and Boolean infinitely divisible measures held at the level of limit theorems of triangular arrays. This result was extended to include…
In this paper we give an analytic interpretation of free convolution of type B, introduced by Biane, Goodman and Nica, and provide a new formula for its computation. This formula allows us to show that free additive convolution of type B is…
The key result in the paper concerns two transformations, Phi(rho, psi) and B_t(psi) on states on the algebra of non-commutative polynomials, or equivalently on joint distributions of d-tuples of non-commuting operators. These…
We study the max-convolution and max-stable laws for Boolean independence and prove that these are Dagum distributions (also known as log-logistical distributions).
We introduce and study a family of $(q,t)$-deformed discrete $N$-particle beta ensembles, where $q$ and $t$ are the parameters of Macdonald polynomials. The main result is the existence of a large-$N$ limit transition leading to random…
We solve two longstanding major problems in Free Probability. This is achieved by generalising the theory to one with values in arbitrary commutative algebras. We prove the existence of the multi-variable $S$-transform, and show that it is…
We investigate the maximal non-critical cluster in a big box in various percolation-type models. We investigate its typical size, and the fluctuations around this typical size. The limit law of these fluctuations are related to maxima of…
In the classical theorems of extreme value theory the limits of suitably rescaled maxima of sequences of independent, identically distributed random variables are studied. So far, only affine rescalings have been considered. We show,…
We obtain upper bounds on the composition length of a finite permutation group in terms of the degree and the number of orbits, and analogous bounds for primitive, quasiprimitive and semiprimitive groups. Similarly, we obtain upper bounds…