Random walks in the high-dimensional limit. I: The Wiener spiral.

DOI10.1214/23-AIHP1406MaRDI QIDQ6663960

Zakhar Kabluchko, Alexander Marynych

Publication date: 15 January 2025

Published in: Annales de l'Institut Henri Poincaré. Probabilités et Statistiques (Search for Journal in Brave)

zbMATH Keywords

random walkscentral limit theoremHausdorff distanceGromov-Hausdorff convergenceWiener spiralrandom metric spacecrinkled arc

Mathematics Subject Classification ID

Geometric probability and stochastic geometry (60D05) Central limit and other weak theorems (60F05) Sums of independent random variables; random walks (60G50)

Cites Work

• Title not available (Why is that?)
• Title not available (Why is that?)
• Title not available (Why is that?)
• Title not available (Why is that?)
• Title not available (Why is that?)
• Convex hulls of random walks and their scaling limits
• Two moments suffice for Poisson approximations: The Chen-Stein method
• Decoupling and Khintchine's inequalities for \(U\)-statistics
• Optimal scaling for various Metropolis-Hastings algorithms.
• The convex hull of a planar random walk: perimeter, diameter, and shape
• A central limit theorem for isotropic random walks on \(n\)-spheres for \(n\to \infty\)
• From Metropolis to diffusions: Gibbs states and optimal scaling.
• Lah distribution: Stirling numbers, records on compositions, and convex hulls of high-dimensional random walks
• Convex hulls of random walks, hyperplane arrangements, and Weyl chambers
• Convex hulls of random walks: expected number of faces and face probabilities
• Wienersche Spiralen und einige andere interessante Kurven im Hilbertschen Raum.
• A course in metric geometry
• Central limit theorems for radial random walks on \(p \times q\) matrices for \(p \to \infty\)
• LIMIT THEOREMS FOR RADIAL RANDOM WALKS ON EUCLIDEAN SPACES OF HIGH DIMENSIONS
• Limit theorems for radial random walks on p × q-matrices as p tends to infinity
• Random Walks in Multidimensional Spaces, Especially on Periodic Lattices
• Limit theorems for uniform distributions on spheres in high-dimensional euclidean spaces
• On the conditions of asymptotic normality of multidimensional randomized decomposable statistics
• On central limit theorems for martingale triangular arrays
• Convex hulls of multidimensional random walks
• High-Dimensional Probability
• Probability: A Graduate Course
• Representation of a Crinkled Arc
• A Crinkled Arc
• Martingale Central Limit Theorems
• Probability

This page was built for publication: Random walks in the high-dimensional limit. I: The Wiener spiral.

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6663960)