A Combinatorial Approach to a Model of Constrained Random Walkers. (16th March 2015)

• Record Type: Journal Article
• Authors: ESPINASSE, T.; GUILLOTIN-PLANTARD, N.; NADEAU, P.
• Is Part Of: Combinatorics, probability and computing. Volume 25:Number 2(2016:Mar.)
• Page Start: 222
• Page End: 235
• Publication Date: 2015-03-16
• Subjects: Primary 60J10, -- Secondary 60F05, -- 05A19; Combinatorial analysis -- Periodicals; Probabilities -- Periodicals; Computer science -- Mathematics -- Periodicals; 511.6
• DOI: 10.1017/S096354831500005X
• Languages: English
• ISSNs: 0963-5483

Abstract

Abstract : In [1 ], the authors consider a random walk ( Z n, 1, . . ., Z n, K +1 ) ∈ ${\mathbb{Z}}$ K +1 with the constraint that each coordinate of the walk is at distance one from the following coordinate. A functional central limit theorem for the first coordinate is proved and the limit variance is explicited. In this paper, we study an extended version of this model by conditioning the extremal coordinates to be at some fixed distance at every time. We prove a functional central limit theorem for this random walk. Using combinatorial tools, we give a precise formula of the variance and compare it with that obtained in [1 ].