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Localization length of the $1+1$ continuum directed random polymer
Publication
, Journal Article
Dunlap, A; Gu, Y; Li, L
Published in: Annales Henri Poincaré
July 2023
In this paper, we study the localization length of the continuum directed polymer, defined as the distance between the endpoints of two paths sampled independently from the quenched polymer measure. We show that the localization length converges in distribution in the thermodynamic limit, and derive an explicit density formula of the limiting distribution. As a consequence, we prove the $\frac32$-power law decay of the density, confirming the physics prediction of Hwa and Fisher (Phys Rev B 49(5):3136, 1994). Our proof uses the recent result of Das and Zhu (Localization of the continuum directed random polymer, 2022).
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Published In
Annales Henri Poincaré
DOI
EISSN
1424-0661
ISSN
1424-0637
Publication Date
July 2023
Volume
24
Issue
7
Start / End Page
2537 / 2555
Publisher
Springer Science and Business Media LLC
Related Subject Headings
- Mathematical Physics
- 5107 Particle and high energy physics
- 5106 Nuclear and plasma physics
- 4902 Mathematical physics
- 0202 Atomic, Molecular, Nuclear, Particle and Plasma Physics
- 0105 Mathematical Physics
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Dunlap, A., Gu, Y., & Li, L. (2023). Localization length of the $1+1$ continuum directed random polymer. Annales Henri Poincaré, 24(7), 2537–2555. https://doi.org/10.1007/s00023-023-01288-z
Dunlap, Alexander, Yu Gu, and Liying Li. “Localization length of the $1+1$ continuum directed random polymer.” Annales Henri Poincaré 24, no. 7 (July 2023): 2537–55. https://doi.org/10.1007/s00023-023-01288-z.
Dunlap A, Gu Y, Li L. Localization length of the $1+1$ continuum directed random polymer. Annales Henri Poincaré. 2023 Jul;24(7):2537–55.
Dunlap, Alexander, et al. “Localization length of the $1+1$ continuum directed random polymer.” Annales Henri Poincaré, vol. 24, no. 7, Springer Science and Business Media LLC, July 2023, pp. 2537–55. Manual, doi:10.1007/s00023-023-01288-z.
Dunlap A, Gu Y, Li L. Localization length of the $1+1$ continuum directed random polymer. Annales Henri Poincaré. Springer Science and Business Media LLC; 2023 Jul;24(7):2537–2555.
![Journal cover image](https://secure.syndetics.com/index.aspx?isbn=/lc.gif&issn=1424-0661&client=dukeuniv)
Published In
Annales Henri Poincaré
DOI
EISSN
1424-0661
ISSN
1424-0637
Publication Date
July 2023
Volume
24
Issue
7
Start / End Page
2537 / 2555
Publisher
Springer Science and Business Media LLC
Related Subject Headings
- Mathematical Physics
- 5107 Particle and high energy physics
- 5106 Nuclear and plasma physics
- 4902 Mathematical physics
- 0202 Atomic, Molecular, Nuclear, Particle and Plasma Physics
- 0105 Mathematical Physics