arXiv subjects

Arundhathi Krishnan

Publications and source records attributed to Arundhathi Krishnan.

3 recordsLinked to original sources

arXiv2024

A central limit theorem in the framework of the Thompson group $F$

We discuss a central limit theorem in the framework of the group algebra of the Thompson group $F$. We consider the sequence of self-adjoint elements given by $a_n=\frac{g_n+g_n^{*}}{\sqrt{2}}$ in the noncommutative probability space $(\mathbb{C}(F),φ)$, where the expectation functional $φ$ is the trace associated to the left regular representation of $F$, and the $g_n$-s are the generators of $F$ in its standard infinite presentation. We show that the limit law of the sequence $s_n = \frac{a_0+\cdots+a_{n-1}}{\sqrt{n}}$ is the standard normal distribution.

math.OA↗

arXiv2022

Markovianity and the Thompson Monoid $F^+$

We introduce a new distributional invariance principle, called `partial spreadability', which emerges from the representation theory of the Thompson monoid $F^+$ in noncommutative probability spaces. We show that a partially spreadable sequence of noncommutative random variables is adapted to a local Markov filtration. Conversely we show that a large class of noncommutative stationary Markov sequences provides representations of the Thompson monoid $F^+$. In the particular case of a classical probability space, we arrive at a de Finetti theorem for stationary Markov sequences with values in a standard Borel space.

math.OA↗

arXiv2022

Markovianity and the Thompson Group $F$

We show that representations of the Thompson group $F$ in the automorphisms of a noncommutative probability space yield a large class of bilateral stationary noncommutative Markov processes. As a partial converse, bilateral stationary Markov processes in tensor dilation form yield representations of $F$. As an application, and building on a result of Kümmerer, we canonically associate a representation of $F$ to a bilateral stationary Markov process in classical probability.

math.OA↗