A New Upper Bound for the Critical Probability of the Frog Model on Homogeneous Trees

被引：6

作者：

Lebensztayn, Elcio ^{[1
]}

Utria, Jaime ^{[2
]}

机构：

[1] Univ Campinas UNICAMP, Inst Math Stat & Sci Computat, Rua Sergio Buarque Holanda 651, BR-13083859 Campinas, SP, Brazil

[2] Fluminense Fed Univ UFF, Inst Math & Stat, Rua Prof Marcos Waldemar Freitas Reis S-N, BR-24210201 Niteroi, RJ, Brazil

来源：

JOURNAL OF STATISTICAL PHYSICS | 2019年 / 176卷 / 01期

基金：

巴西圣保罗研究基金会;

关键词：

Frog model; Homogeneous tree; Critical probability; RECURRENCE; TRANSIENCE;

D O I：

10.1007/s10955-019-02294-4

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We consider the interacting particle system on the homogeneous tree of degree (d+1), known as frog model. In this model, active particles perform independent random walks, awakening all sleeping particles they encounter, and dying after a random number of jumps, with geometric distribution. We prove an upper bound for the critical parameter of survival of the model, which improves the previously known results. This upper bound was conjectured in a paper by Lebensztayn et al. (J Stat Phys 119(1-2):331-345, 2005). We also give a closed formula for the upper bound.

引用

页码：169 / 179

页数：11

共 50 条

[41] RECURRENCE AND TRANSIENCE FOR THE FROG MODEL ON TREES
Hoffman, Christopher
Johnson, Tobias
Junge, Matthew
ANNALS OF PROBABILITY, 2017, 45 (05): : 2826 - 2854
[42] A statistical model to estimate an upper bound on the probability of failure of a system installed on an irradiated vehicle
Konefal, Tadeusz
Marvin, Andy C.
Dawson, John F.
Robinson, Martin P.
IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY, 2007, 49 (04) : 840 - 848
[43] A New Upper Bound on Cache Hit Probability for Non-Anticipative Caching Policies
Panigrahy, Nitish K.
Nain, Philippe
Neglia, Giovanni
Towsley, Don
ACM TRANSACTIONS ON MODELING AND PERFORMANCE EVALUATION OF COMPUTING SYSTEMS, 2022, 7 (2-4)
[44] A new upper bound on the block error probability after decoding over the erasure channel
Didier, Frederic
IEEE TRANSACTIONS ON INFORMATION THEORY, 2006, 52 (10) : 4496 - 4503
[45] A New Upper Bound on Cache Hit Probability for Non-anticipative Caching Policies
Panigrahy N.K.
Nain P.
Neglia G.
Towsley D.
Performance Evaluation Review, 2021, 48 (03): : 138 - 143
[46] An upper bound for the probability of visiting a distant point by a critical branching random walk in Z4
Zhu, Qingsan
ELECTRONIC COMMUNICATIONS IN PROBABILITY, 2019, 24
[47] An efficient upper bound of the rotation distance of binary trees
Pallo, J
INFORMATION PROCESSING LETTERS, 2000, 73 (3-4) : 87 - 92
[48] A sharp upper bound for the number of spanning trees of a graph
Das, Kinkar Ch.
GRAPHS AND COMBINATORICS, 2007, 23 (06) : 625 - 632
[49] ON TREES ATTAINING AN UPPER BOUND ON THE TOTAL DOMINATION NUMBER
Krzywkowski, M.
BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY, 2015, 41 (06) : 1339 - 1344
[50] On the upper bound for the number of spanning trees of a connected graph
Li, Rao
Journal of Combinatorial Mathematics and Combinatorial Computing, 2015, 95 : 257 - 269

← 1 2 3 4 5 →