On the $x$-$y$ Symmetry of Correlators in Topological Recursion via Loop Insertion Operator
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866909307025489920 |
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| author | Hock, Alexander |
| author_facet | Hock, Alexander |
| contents | Topological Recursion generates a family of symmetric differential forms (correlators) from some initial data $(Σ,x,y,B)$. We give a functional relation between the correlators of genus $g=0$ generated by the initial data $(Σ,x,y,B)$ and by the initial data $(Σ,y,x,B)$, where $x$ and $y$ are interchanged. The functional relation is derived with the loop insertion operator by computing a functional relation for some intermediate correlators. Additionally, we show that our result is equivalent to the recent result of \cite{Borot:2021thu} in case of $g=0$. Consequently, we are providing a simplified functional relation between generating series of higher order free cumulants and moments in higher order free probability. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2201_05357 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On the $x$-$y$ Symmetry of Correlators in Topological Recursion via Loop Insertion Operator Hock, Alexander Mathematical Physics Combinatorics Probability 46L54, 15B52, 16R60, 05A18 Topological Recursion generates a family of symmetric differential forms (correlators) from some initial data $(Σ,x,y,B)$. We give a functional relation between the correlators of genus $g=0$ generated by the initial data $(Σ,x,y,B)$ and by the initial data $(Σ,y,x,B)$, where $x$ and $y$ are interchanged. The functional relation is derived with the loop insertion operator by computing a functional relation for some intermediate correlators. Additionally, we show that our result is equivalent to the recent result of \cite{Borot:2021thu} in case of $g=0$. Consequently, we are providing a simplified functional relation between generating series of higher order free cumulants and moments in higher order free probability. |
| title | On the $x$-$y$ Symmetry of Correlators in Topological Recursion via Loop Insertion Operator |
| topic | Mathematical Physics Combinatorics Probability 46L54, 15B52, 16R60, 05A18 |
| url | https://arxiv.org/abs/2201.05357 |