Covering a Connected Curve on the Torus with Squares

Shang Yuan Shiu

doi:10.1007/s10959-011-0387-y

Covering a Connected Curve on the Torus with Squares

Shang Yuan Shiu

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We throw i. i. d. random squares S₁,S₂, ... with respective side lengths l₁,l₂, ... uniformly on the two-dimensional torus ℝ/ℤ×ℝ/ℤ, where {l_n}^∞_n=1 is a nonincreasing sequence with 0<l_n<1 and lim_n→∞l_n = 0. A necessary and sufficient condition for covering the connected curve {0}×ℝ/ℤ is,.

Original language	English
Pages (from-to)	480-488
Number of pages	9
Journal	Journal of Theoretical Probability
Volume	26
Issue number	2
DOIs	https://doi.org/10.1007/s10959-011-0387-y
State	Published - Jun 2013

Keywords

Random covering

Access to Document

10.1007/s10959-011-0387-y

Cite this

@article{56015ad9e7f94aa89eb908a4886ed262,

title = "Covering a Connected Curve on the Torus with Squares",

abstract = "We throw i. i. d. random squares S1,S2, ... with respective side lengths l1,l2, ... uniformly on the two-dimensional torus ℝ/ℤ×ℝ/ℤ, where {ln}∞n=1 is a nonincreasing sequence with 0n<1 and limn→∞ln = 0. A necessary and sufficient condition for covering the connected curve {0}×ℝ/ℤ is,.",

keywords = "Random covering",

author = "Shiu, {Shang Yuan}",

year = "2013",

month = jun,

doi = "10.1007/s10959-011-0387-y",

language = "???core.languages.en_GB???",

volume = "26",

pages = "480--488",

journal = "Journal of Theoretical Probability",

issn = "0894-9840",

number = "2",

}

TY - JOUR

T1 - Covering a Connected Curve on the Torus with Squares

AU - Shiu, Shang Yuan

PY - 2013/6

Y1 - 2013/6

N2 - We throw i. i. d. random squares S1,S2, ... with respective side lengths l1,l2, ... uniformly on the two-dimensional torus ℝ/ℤ×ℝ/ℤ, where {ln}∞n=1 is a nonincreasing sequence with 0n<1 and limn→∞ln = 0. A necessary and sufficient condition for covering the connected curve {0}×ℝ/ℤ is,.

AB - We throw i. i. d. random squares S1,S2, ... with respective side lengths l1,l2, ... uniformly on the two-dimensional torus ℝ/ℤ×ℝ/ℤ, where {ln}∞n=1 is a nonincreasing sequence with 0n<1 and limn→∞ln = 0. A necessary and sufficient condition for covering the connected curve {0}×ℝ/ℤ is,.

KW - Random covering

UR - http://www.scopus.com/inward/record.url?scp=84878114964&partnerID=8YFLogxK

U2 - 10.1007/s10959-011-0387-y

DO - 10.1007/s10959-011-0387-y

M3 - 期刊論文

AN - SCOPUS:84878114964

SN - 0894-9840

VL - 26

SP - 480

EP - 488

JO - Journal of Theoretical Probability

JF - Journal of Theoretical Probability

IS - 2

ER -

Covering a Connected Curve on the Torus with Squares

Abstract

Keywords

Access to Document

Fingerprint

Cite this