Diffusivity of a random walk on random walks. Issue 2 (16th April 2014)

• Record Type: Journal Article
• Authors: Boissard, Emmanuel; Cohen, Serge; Espinasse, Thibault; Norris, James
• Is Part Of: Random structures & algorithms. Volume 47:Issue 2(2015)
• Page Start: 267
• Page End: 283
• Publication Date: 2014-04-16
• Subjects: Random graphs -- Periodicals; Mathematical analysis -- Periodicals; 519
• DOI: 10.1002/rsa.20541
• Languages: English
• ISSNs: 1042-9832

Abstract

<abstract abstract-type="main"> <title>Abstract</title> <p>We consider a random walk <inline-formula><alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgj23twfzz7" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math display="inline" altimg="urn:x-wiley::media:rsa20541:rsa20541-math-0001" overflow="scroll" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msubsup><mml:mi>Z</mml:mi><mml:mi>n</mml:mi><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:msubsup><mml:mo>, </mml:mo><mml:mo>…</mml:mo><mml:mo>, </mml:mo><mml:msubsup><mml:mi>Z</mml:mi><mml:mi>n</mml:mi><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mi>K</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:msubsup></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>∈</mml:mo><mml:msup><mml:mo>ℤ</mml:mo><mml:mrow><mml:mi>K</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></alternatives></inline-formula> with the constraint that each coordinate of the walk is at distance one from the following one. In this paper, we show that this random walk is slowed down by a variance factor <inline-formula><alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgj23twg02w" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math display="inline" altimg="urn:x-wiley::media:rsa20541:rsa20541-math-0002" overflow="scroll" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msubsup><mml:mo>σ</mml:mo><mml:mi>K</mml:mi><mml:mn>2</mml:mn></mml:msubsup><mml:mo>=</mml:mo><mml:mfrac><mml:mn>2</mml:mn><mml:mrow><mml:mi>K</mml:mi><mml:mo>+</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:mfrac></mml:mrow></mml:math></alternatives></inline-formula> with respect to the case of the classical simple random walk without constraint. © 2014 Wiley Periodicals, Inc. Random Struct. Alg., 47, 267–283, 2015</p> </abstract>