Fluctuation lower bounds in planar random growth models

被引：1

作者：

Bates, Erik ^{[1
]}

Chatterjee, Sourav ^{[2
]}

机构：

[1] Univ Calif Berkeley, Dept Math, 1067 Evans Hall, Berkeley, CA 94720 USA

[2] Stanford Univ, Dept Stat, Sequoia Hall,390 Jane Stanford Way, Stanford, CA 94305 USA

来源：

ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES | 2020年 / 56卷 / 04期

关键词：

First-passage percolation; Corner growth model; Directed polymers; 1ST PASSAGE PERCOLATION; DIMENSIONAL DIRECTED POLYMER; 1ST-PASSAGE PERCOLATION; SHAPE FLUCTUATIONS; ORIENTED PERCOLATION; RANDOM ENVIRONMENT; LIMITING-SHAPE; TIME CONSTANT; DIVERGENCE; DISTRIBUTIONS;

D O I：

10.1214/19-AIHP1043

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We prove root log n lower bounds on the order of growth fluctuations in three planar growth models (first-passage percolation, last-passage percolation, and directed polymers) under no assumptions on the distribution of vertex or edge weights other than the minimum conditions required for avoiding pathologies. Such bounds were previously known only for certain restrictive classes of distributions. In addition, the first-passage shape fluctuation exponent is shown to be at least 1/8, extending previous results to more general distributions.

引用

页码：2406 / 2427

页数：22

共 50 条

[41] A GENERAL METHOD FOR LOWER BOUNDS ON FLUCTUATIONS OF RANDOM VARIABLES
Chatterjee, Sourav
ANNALS OF PROBABILITY, 2019, 47 (04): : 2140 - 2171
[42] New lower bounds on subgroup growth and homology growth
Lackenby, Marc
PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, 2009, 98 : 271 - 297
[43] Lower bounds for dynamic programming on planar graphs of bounded cutwidth
van Geffen B.A.M.
Jansen B.M.P.
Kroon A.A.W.M.
Morel R.
Journal of Graph Algorithms and Applications, 2020, 24 (03) : 461 - 482
[44] Geometric dilation of closed planar curves:: New lower bounds
Ebbers-Baumann, Annette
Gruene, Ansgar
Klein, Rolf
COMPUTATIONAL GEOMETRY-THEORY AND APPLICATIONS, 2007, 37 (03): : 188 - 208
[45] Lower bounds for expected-case planar point location
Malamatos, Theocharis
COMPUTATIONAL GEOMETRY-THEORY AND APPLICATIONS, 2008, 39 (02): : 91 - 103
[46] Improved Lower and Upper Bounds for Universal TSP in Planar Metrics
Hajiaghayi, Mohammad T.
Kleinberg, Robert
Leighton, Tom
PROCEEDINGS OF THE SEVENTHEENTH ANNUAL ACM-SIAM SYMPOSIUM ON DISCRETE ALGORITHMS, 2006, : 649 - 658
[47] Regression models using the LINEX loss to predict lower bounds for the number of points for approximating planar contour shapes
Jayasinghe, J. M. Thilini
Ellingson, Leif
Prematilake, Chalani
JOURNAL OF APPLIED STATISTICS, 2022, 49 (16) : 4294 - 4313
[48] SATURATION OF UNITARITY BOUNDS IN PLANAR AND NON-PLANAR MODELS OF MULTIPARTICLE RESCATTERING
SCHWIMME.A
VENEZIAN.G
NUCLEAR PHYSICS B, 1974, B 81 (03) : 445 - 457
[49] Fluctuation results for Hastings-Levitov planar growth
Silvestri, Vittoria
PROBABILITY THEORY AND RELATED FIELDS, 2017, 167 (1-2) : 417 - 460
[50] Fluctuation theory of connectivities for subcritical random cluster models
Campanino, Massimo
Ioffe, Dmitry
Velenik, Yvan
ANNALS OF PROBABILITY, 2008, 36 (04): : 1287 - 1321

← 1 2 3 4 5 →