The subleading order of two dimensional cover times

被引：28
|
作者：
Belius, David [1 ]
Kistler, Nicola [2 ]
机构：
[1] NYU, Courant Inst Math Sci, 251 Mercer St, New York, NY 10012 USA
[2] Goethe Univ Frankfurt, Inst Math, D-60054 Frankfurt, Germany
来源：
PROBABILITY THEORY AND RELATED FIELDS | 2017年 / 167卷 / 1-2期
基金：
瑞士国家科学基金会;
关键词：
BROWNIAN-MOTION; 2; DIMENSIONS; RANDOM-WALKS; ASYMPTOTICS; TREES;
D O I：
10.1007/s00440-015-0689-6
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：
The -cover time of the two dimensional torus by Brownian motion is the time it takes for the process to come within distance from any point. Its leading order in the small -regime has been established by Dembo et al. (Ann Math 160:433-464, 2004). In this work, the second order correction is identified. The approach relies on a multi-scale refinement of the second moment method, and draws on ideas from the study of the extremes of branching Brownian motion.
引用
收藏
页码：461 / 552
页数：92
相关论文
共 50 条
  • [1] The subleading order of two dimensional cover times
    David Belius
    Nicola Kistler
    [J]. Probability Theory and Related Fields, 2017, 167 : 461 - 552
  • [2] Generalised scaling at subleading order
    Freyhult, Lisa
    [J]. JOURNAL OF HIGH ENERGY PHYSICS, 2012, (01):
  • [3] Generalised scaling at subleading order
    Lisa Freyhult
    [J]. Journal of High Energy Physics, 2012
  • [4] Signal at subleading order in lattice HQET
    Dürr, S
    Jüttner, A
    Rolf, J
    Sommer, R
    [J]. NUCLEAR PHYSICS B-PROCEEDINGS SUPPLEMENTS, 2005, 140 : 488 - 490
  • [5] Plasma stopping power including subleading order
    Brown, Lowell S.
    Preston, Dean L.
    Singleton, Robert L., Jr.
    [J]. JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 2006, 39 (17): : 4667 - 4670
  • [6] Two dimensional distribution of relaxation times
    Mikonis, A.
    Banys, J.
    Grigalaitis, R.
    Lapinskas, S.
    Matulis, A.
    Voelkel, G.
    [J]. FERROELECTRICS, 2007, 353 : 588 - +
  • [7] Cover times for Brownian motion and random walks in two dimensions
    Dembo, A
    Peres, Y
    Rosen, J
    Zeitouni, O
    [J]. ANNALS OF MATHEMATICS, 2004, 160 (02) : 433 - 464
  • [8] Five-dimensional relativity and two times
    Wesson, PS
    [J]. PHYSICS LETTERS B, 2002, 538 (1-2) : 159 - 163
  • [9] Correction to: Tightness for the cover time of the two dimensional sphere
    David Belius
    Jay Rosen
    Ofer Zeitouni
    [J]. Probability Theory and Related Fields, 2020, 176 : 1439 - 1444
  • [10] COVER TIMES FOR MARKOV-GENERATED BINARY SEQUENCES OF LENGTH TWO
    Fisher, Evan
    Huang, Tianman
    Wang, Xiaoshi
    [J]. ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, 2020, 50 (03) : 957 - 974
12345