Zobrazeno 1 - 10
of 43
pro vyhledávání: '"Alan Hammond"'
Publikováno v:
Forum of Mathematics, Sigma, Vol 11 (2023)
For an n-element subset U of $\mathbb {Z}^2$ , select x from U according to harmonic measure from infinity, remove x from U and start a random walk from x. If the walk leaves from y when it first enters the rest of U, add y to it. Iterating this pr
Externí odkaz:
https://doaj.org/article/c43fadd64df248c18b8870b43d7a3a2a
Autor:
ALAN HAMMOND
Publikováno v:
Forum of Mathematics, Pi, Vol 7 (2019)
In last passage percolation models lying in the Kardar–Parisi–Zhang (KPZ) universality class, the energy of long energy-maximizing paths may be studied as a function of the paths’ pair of endpoint locations. Scaled coordinates may be introduced
Externí odkaz:
https://doaj.org/article/910b4f266d904002b2cf322b8393c47e
Publikováno v:
Electronic Journal of Probability. 28
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::d724653261924e11e14fde418895cf07
https://doi.org/10.1214/22-ejp898
https://doi.org/10.1214/22-ejp898
Autor:
Alan Hammond
Publikováno v:
Proceedings of the London Mathematical Society. 120:370-433
In last passage percolation models lying in the KPZ universality class, long maximizing paths have a typical deviation from the linear interpolation of their endpoints governed by the two-thirds power of the interpolating distance. This two-thirds po
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::1d9b8cbd88df331f2047d85ff16e6df5
https://doi.org/10.1112/plms.12292
https://doi.org/10.1112/plms.12292
Publikováno v:
Ann. Probab. 49, no. 1 (2021), 485-505
In last passage percolation models lying in the Kardar-Parisi-Zhang universality class, maximizing paths that travel over distances of order $n$ accrue energy that fluctuates on scale $n^{1/3}$; and these paths deviate from the linear interpolation o
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::aecee34971ed54c8045ecf1ad780cca1
https://doi.org/10.1214/20-aop1444
https://doi.org/10.1214/20-aop1444
Autor:
Shirshendu Ganguly, Alan Hammond
The energy and geometry of maximizing paths in integrable last passage percolation models are governed by the characteristic KPZ scaling exponents of one-third and two-thirds. When represented in scaled coordinates that respect these exponents, this
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a6065c312bd437c69e27f52e1c611877
http://arxiv.org/abs/2010.05836
http://arxiv.org/abs/2010.05836
Autor:
Alan Hammond, Sourav Sarkar
Publikováno v:
Electron. J. Probab.
In last passage percolation models, the energy of a path is maximized over all directed paths with given endpoints in a random environment, and the maximizing paths are called geodesics. The geodesics and their energy can be scaled so that transforme
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::4e6c4974c5d7515f6afba61ffab4577b
https://projecteuclid.org/euclid.ejp/1582534894
https://projecteuclid.org/euclid.ejp/1582534894
Autor:
Alan Hammond
Publikováno v:
Ann. Probab. 47, no. 6 (2019), 3911-3962
In last passage percolation models lying in the KPZ universality class, the energy of long energy-maximizing paths may be studied as a function of the paths' pair of endpoint locations. Scaled coordinates may be introduced, so that these maximizing p
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::4015c6bbd13dfa699c5094d336f9c5ac
https://doi.org/10.1214/19-aop1350
https://doi.org/10.1214/19-aop1350
Autor:
Alan Hammond
Publikováno v:
Electron. J. Probab.
For $d \geq 2$ and $n \in \mathbb{N}$, let $\mathsf{W}_n$ denote the uniform law on self-avoiding walks beginning at the origin in the integer lattice $\mathbb{Z}^d$, and write $\Gamma$ for a $\mathsf{W}_n$-distributed walk. We show that the closing
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::8da693e8ce544c63ce49009fa5ae01ba
https://projecteuclid.org/euclid.ejp/1558404407
https://projecteuclid.org/euclid.ejp/1558404407