We investigate the hydrodynamic behavior of zeroes of trigonometric polynomials under
repeated differentiation. We show that if the zeroes of a real-rooted, degree $ d …

The backward heat flow on the real line started from the initial condition $ z^ n $ results in
the classical $ n $-th Hermite polynomial whose zeroes are distributed according to the …

The $\mathcal {A} $-tracial algebras are algebras endowed with multi-linear forms,
compatible with the product, and indexed by partitions. Using the notion of $\mathcal {A} …

We provide a refined combinatorial identity for the set of partitions of, which plays an
important role in investigating several limit theorems related to finite free convolutions …

The master field is the large N limit of the Yang–Mills measure on the Euclidean plane. It can
be viewed as a non-commutative process indexed by loops on the plane. We construct and …

We study states on the universal noncommutative⁎-algebra generated by the coefficients of
a unitary matrix, or equivalently states on the unitary dual group. Its structure of dual group in …

The wrapping transformation is a homomorphism from the semigroup of probability
measures on the real line, with the convolution operation, to the semigroup of probability …

We establish a link between free probability theory and Witt vectors, via the theory of formal
groups. We derive an exponential isomorphism which expresses Voiculescu's free …

This paper defines the notion of generators for a class of decreasing radial Loewner chains
that are only continuous with respect to time. For this purpose,“Loewner's integral equation” …

We consider different limit theorems for additive and multiplicative free Lévy processes. The
main results are concerned with positive and unitary multiplicative free Lévy processes at …