## Subsequential scaling limits for Liouville graph distance

Publication
, Journal Article

Ding, J; Dunlap, A

Published in: Communications in Mathematical Physics

June 1, 2020

For $0 < γ< 2$ and $δ> 0$, we consider the Liouville graph distance, which is the minimal number of Euclidean balls of $γ$-Liouville quantum gravity measure at most $δ$ whose union contains a continuous path between two endpoints. In this paper, we show that the renormalized distance is tight and thus has subsequential scaling limits at $δ→ 0$. In particular, we show that for all $δ> 0$ the diameter with respect to the Liouville graph distance has the same order as the typical distance between two endpoints.

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## Published In

Communications in Mathematical Physics

## DOI

## EISSN

1432-0916

## ISSN

0010-3616

## Publication Date

June 1, 2020

## Volume

376

## Issue

2

## Start / End Page

1499 / 1572

## Related Subject Headings

- Mathematical Physics
- 5107 Particle and high energy physics
- 4904 Pure mathematics
- 4902 Mathematical physics
- 0206 Quantum Physics
- 0105 Mathematical Physics
- 0101 Pure Mathematics

### Citation

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Ding, J., & Dunlap, A. (2020). Subsequential scaling limits for Liouville graph distance.

*Communications in Mathematical Physics*,*376*(2), 1499–1572. https://doi.org/10.1007/s00220-020-03684-6Ding, Jian, and Alexander Dunlap. “Subsequential scaling limits for Liouville graph distance.”

*Communications in Mathematical Physics*376, no. 2 (June 1, 2020): 1499–1572. https://doi.org/10.1007/s00220-020-03684-6.Ding J, Dunlap A. Subsequential scaling limits for Liouville graph distance. Communications in Mathematical Physics. 2020 Jun 1;376(2):1499–572.

Ding, Jian, and Alexander Dunlap. “Subsequential scaling limits for Liouville graph distance.”

*Communications in Mathematical Physics*, vol. 376, no. 2, June 2020, pp. 1499–572.*Manual*, doi:10.1007/s00220-020-03684-6.Ding J, Dunlap A. Subsequential scaling limits for Liouville graph distance. Communications in Mathematical Physics. 2020 Jun 1;376(2):1499–1572.

## Published In

Communications in Mathematical Physics

## DOI

## EISSN

1432-0916

## ISSN

0010-3616

## Publication Date

June 1, 2020

## Volume

376

## Issue

2

## Start / End Page

1499 / 1572

## Related Subject Headings

- Mathematical Physics
- 5107 Particle and high energy physics
- 4904 Pure mathematics
- 4902 Mathematical physics
- 0206 Quantum Physics
- 0105 Mathematical Physics
- 0101 Pure Mathematics