The height and range of watermelons without wall

We determine the weak limit of the distribution of the random variables "height" and "range" on the set of p -watermelons without wall restriction as the number of steps tends to infinity. Additionally, we provide asymptotics for the moments of the random variable "height".

• Publication year

  2008

• Venue

  European journal of combinatorics (Print)

• Publication date

  2008-05-30

• Fields of study

  Mathematics, Physics, Computer Science

• Identifiers
  DOI 10.1007/978-3-642-10217-2_25arXiv 0806.0037
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

• The Height and Range of Watermelons without Wall

  2008cited by this paper
• Exact distribution of the maximal height of watermelons

  2008cited by this paper
• The height of watermelons with wall

  2008influential reference
• Maximum distributions of bridges of noncolliding Brownian paths.

  2008cited by this paper
• Exact distribution of the maximal height of p vicious walkers.

  2008cited by this paper
• Watermelon uniform random generation with applications

  2003cited by this paper
• Asymptotic behaviour of watermelons

  2003cited by this paper
• Functional central limit theorems for vicious walkers

  2002cited by this paper
• Vicious random walkers and a discretization of Gaussian random matrix ensembles

  2001cited by this paper
• Vicious walkers, friendly walkers and Young tableaux: II. With a wall

  2000cited by this paper
• Random vicious walks and random matrices

  2000cited by this paper
• Non-intersecting paths, random tilings and random matrices

  2000cited by this paper
• ADVANCED DETERMINANT CALCULUS

  1999cited by this paper
• Vicious walkers and Young tableaux I: without walls

  1998cited by this paper
• Vicious walkers and directed polymer networks in general dimensions.

  1995cited by this paper
• Mellin Transforms and Asymptotics: Harmonic Sums

  1995cited by this paper
• Determinants, Paths, and Plane Partitions

  1989cited by this paper
• Walks, walls, wetting, and melting

  1984cited by this paper
• A Relation between Brownian Bridge and Brownian Excursion

  1979cited by this paper
• Excursions in Brownian motion

  1976cited by this paper
• The distribution of the maximum Brownian excursion

  1976cited by this paper
• On orthogonal polynomials

  1975cited by this paper
• On the Vector Representations of Induced Matroids

  1973influential reference

• Composition Schemes: q-Enumerations and Phase Transitions in Gibbs Models

  2023cites this paper
• Contacts and returns in 2-watermelons without wall

  2020influential citation
• Extreme value statistics of correlated random variables: A pedagogical review

  2019cites this paper
• Invariance principles for random walks in cones

  2015influential citation
• Non-intersecting Brownian bridges and the Laguerre Orthogonal Ensemble

  2015cites this paper
• PR ] 2 4 M ar 2 01 1 Bessel process , Schramm-Loewner evolution , and Dyson model – Complex Analysis applied to Stochastic Processes and Statistical Mechanics – ∗

  2013cites this paper
• Airy processes and variational problems

  2013cites this paper
• Communications in Mathematical Physics Continuum Statistics of the Airy 2 Process

  2013cites this paper
• Brownian Gibbs property for Airy line ensembles

  2013cites this paper
• Extreme value distributions of noncolliding diffusion processes (Spectra of Random Operators and Related Topics)

  2011cites this paper
• Brownian Gibbs property for Airy line ensembles

  2011cites this paper
• Endpoint Distribution of Directed Polymers in 1 + 1 Dimensions

  2011cites this paper
• Extreme value distributions of noncolliding diffusion processes

  2010cites this paper
• The height of watermelons with wall

  2008cites this paper