Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An alternating moment condition for bi-freeness   In this note we demonstrate an equivalent condition for bi-freeness, inspired
by the well-known "vanishing of alternating centred moments" condition from
free probability. We show that all products satisfying a centred condition on
maximal monochromatic \chi-intervals have vanishing moments if and only if the
family of pairs of faces they come from is bi-free, and show that similar
characterisations hold for the amalgamated and conditional settings. In
addition, we construct a bi-free unitary Brownian motion and show that
conjugation by this process asymptotically creates bi-freeness; these
considerations lead to another characterisation of bi-free independence.

14
The categories of this paper are: math-ph
17
The categories of this paper are: q-fin
7
The categories of this paper are: hep-th
33
The categories of this paper are: plasm-ph
27
The categories of this paper are: comp-gas
3
The categories of this paper are: physics
21
The categories of this paper are: adap-org
29
The categories of this paper are: funct-an
10
The categories of this paper are: q-bio
16
The categories of this paper are: stat
32
The categories of this paper are: atom-ph
1
The categories of this paper are: cs
30
The categories of this paper are: q-alg
12
The categories of this paper are: nucl-th
0
The categories of this paper are: hep-ph
34
The categories of this paper are: chem-ph