Backbone scaling limits for random walks on random critical trees

被引：0

作者：

Ben Arous, Gerard ^{[1
]}

Cabezas, Manuel ^{[2
]}

Fribergh, Alexander ^{[3
]}

机构：

[1] New York Univ, Courant Inst Math Sci, 251 Mercer St, New York, NY 10012 USA

[2] Pontificia Univ Catolica Chile, Ave Vicuna Mackenna 4860, Santiago, Chile

[3] Univ Montreal, DMS, Pavillon Andre Aisenstadt 2920,chemin Tour, Montreal, PQ H3T 1J4, Canada

来源：

ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES | 2024年 / 60卷 / 03期

基金：

加拿大自然科学与工程研究理事会;

关键词：

Percolation; Random walk; INVASION PERCOLATION; INVARIANCE-PRINCIPLE; BROWNIAN-MOTION;

D O I：

10.1214/23-AIHP1394

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 the existence of scaling limits for the projection on the backbone of the random walks on the Incipient Infinite Cluster and the Invasion Percolation Cluster on a regular tree. We treat these projected random walks as Randomly trapped random walks (as defined in ) and thus describe these scaling limits as spatially subordinated Brownian motions.

引用

页码：1814 / 1848

页数：35

共 50 条

[1] SCALING LIMITS FOR SIMPLE RANDOM WALKS ON RANDOM ORDERED GRAPH TREES
Croydon, D. A.
[J]. ADVANCES IN APPLIED PROBABILITY, 2010, 42 (02) : 528 - 558
[2] Scaling for random walks on Eden trees
Reis, FDAA
[J]. PHYSICAL REVIEW E, 1996, 54 (04) : R3079 - R3081
[3] Scaling for random walks on Eden trees
[J]. Phys Rev E., 4-A pt A (R3079):
[4] Scaling limits of loop-erased random walks and uniform spanning trees
Oded Schramm
[J]. Israel Journal of Mathematics, 2000, 118 : 221 - 288
[5] Scaling limits of loop-erased random walks and uniform spanning trees
Schramm, O
[J]. ISRAEL JOURNAL OF MATHEMATICS, 2000, 118 (1) : 221 - 288
[6] Convex hulls of random walks and their scaling limits
Wade, Andrew R.
Xu, Chang
[J]. STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2015, 125 (11) : 4300 - 4320
[7] Scaling limits of random Polya trees
Panagiotou, Konstantinos
Stufler, Benedikt
[J]. PROBABILITY THEORY AND RELATED FIELDS, 2018, 170 (3-4) : 801 - 820
[8] Scaling limit of critical random trees in random environment
Conchon-Kerjan, Guillaume
Kious, Daniel
Mailler, Cecile
[J]. ELECTRONIC JOURNAL OF PROBABILITY, 2024, 29
[9] Critical scaling in standard biased random walks
Anteneodo, C.
Morgado, W. A. M.
[J]. PHYSICAL REVIEW LETTERS, 2007, 99 (18)
[10] Scaling limits of recurrent excited random walks on integers
Dolgopyat, Dmitry
Kosygina, Elena
[J]. ELECTRONIC COMMUNICATIONS IN PROBABILITY, 2012, 17 : 1 - 14

← 1 2 3 4 5 →