Vicious walkers, friendly walkers and Young tableaux II: With a wall

Abstract

We derive new results for the number of star and watermelon configurations of vicious walkers in the presence of an impenetrable wall by showing that these follow from standard results in the theory of Young tableaux, and combinatorial descriptions of symmetric functions. For the problem of $n$-friendly walkers, we derive exact asymptotics for the number of stars and watermelons both in the absence of a wall and in the presence of a wall.

35 pages, AmS-LaTeX; Definitions of n-friendly walkers clarified; the statement of Theorem 4 and its proof were corrected

References in corpus (2)

• Universal Distributions for Growth Processes in 1+1 Dimensions and Random Matrices
• Statistical Self-Similarity of One-Dimensional Growth Processes

Cited by in corpus (53)

• Persistence and First-Passage Properties in Non-equilibrium Systems
• Non-intersecting Brownian walkers and Yang-Mills theory on the sphere
• Symmetry of matrix-valued stochastic processes and noncolliding diffusion particle systems
• Why Delannoy numbers?
• Exact distribution of the maximal height of p vicious walkers
• Scaling limit of vicious walks and two-matrix model
• Nonintersecting Brownian excursions
• Cylindric versions of specialised Macdonald functions and a deformed Verlinde algebra
• Noncolliding Brownian Motion and Determinantal Processes
• Reunion probability of N vicious walkers: typical and large fluctuations for large N
• Vicious walk with a wall, noncolliding meanders, and chiral and Bogoliubov-deGennes random matrices
• Dynamical Correlations among Vicious Random Walkers
• Maximum distributions of bridges of noncolliding Brownian paths
• Vicious Random Walkers and a Discretization of Gaussian Random Matrix Ensembles
• Functional central limit theorems for vicious walkers
• Orbit measures, random matrix theory and interlaced determinantal processes
• Two Bessel Bridges Conditioned Never to Collide, Double Dirichlet Series, and Jacobi Theta Function
• Families of Vicious Walkers
• Vicious Walkers in a Potential
• Ordering of Random Walks: The Leader and the Laggard
• First-encounter time of two diffusing particles in confinement
• Non-intersecting Brownian bridges in the flat-to-flat geometry
• Interacting Particles on the Line and Dunkl Intertwining Operator of Type A: Application to the Freezing Regime
• Non-crossing Brownian paths and Dyson Brownian motion under a moving boundary
• The height of watermelons with wall
• Correlation Functions of XX0 Heisenberg Chain, q-Binomial Determinants, and Random Walks
• Dynamical Correlations for Vicious Random Walk with a Wall
• Watermelon configurations with wall interaction: exact and asymptotic results
• Discrete analogues of Macdonald-Mehta integrals
• Intermediate disorder directed polymers and the multi-layer extension of the stochastic heat equation
• The correlation functions of the XX Heisenberg magnet and random walks of vicious walkers
• O'Connell's process as a vicious Brownian motion
• Dynamical phase transition in the occupation fraction statistics for non-crossing Brownian particles
• Noncolliding Brownian Motion with Drift and Time-Dependent Stieltjes-Wigert Determinantal Point Process
• Optimal potentials for diffusive search strategies
• Random walks and random fixed-point free involutions
• Three osculating walkers
• The Ising Limit of the XXZ Heisenberg Magnet and Certain Thermal Correlation Functions
• Two-step asymptotics of scaled Dunkl processes
• From Vicious Walkers to TASEP
• Maximal distance travelled by N vicious walkers till their survival
• Constant term solution for an arbitrary number of osculating lattice paths
• The height and range of watermelons without wall
• Plane partitions of shifted double staircase shape
• Moments of vicious walkers and Möbius graph expansions
• Skew Howe duality and limit shapes of Young diagrams
• Correlation Functions as Nests of Self-Avoiding Paths
• Constrained non-crossing Brownian motions, fermions and the Ferrari-Spohn distribution
• Dynamics of unvisited sites in presence of mutually repulsive random walkers
• Unitary matrix integrals, symmetric polynomials, and long-range random walks
• Linear recurrences for cylindrical networks
• Three friendly walkers
• Spin correlation functions, Ramus-like identities, and enumeration of constrained lattice walks and plane partitions