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arXiv · 2304.10617

Statistical Fluctuation of Infinitesimal Spaces

Damien Tageddine·Jean-Christophe Nave
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Abstract

This paper is a follow-up on the \emph{noncommutative differential geometry on infinitesimal spaces} [15]. In the present work, we extend the algebraic convergence from [15] to the geometric setting. On the one hand, we reformulate the definition of finite dimensional compatible Dirac operators using Clifford algebras. This definition also leads to a new construction of a Laplace operator. On the other hand, after a well-chosen Green's function defined on a manifold, we show that when the Dirac operators can be interpreted as stochastic matrices. The sequence $(D_n)_{n\in \mathbb{N}}$ converges then in average to the usual Dirac operator on a spin manifold. The same conclusion can be drawn for the Laplace operator.

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BibTeXRIS

Damien Tageddine, Jean-Christophe Nave. 2023-04-20. Statistical Fluctuation of Infinitesimal Spaces. https://arxiv.org/abs/2304.10617

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