GUE Fluctuations Near the Axis in One-Sided Ballistic Deposition

2025/04/22 by Pablo Groisman, Groisman, Pablo, Alejandro F. Ramı́rez +5
Engineering · Physics and Astronomy · #60K35 #82C41 #Atomic and Molecular Physics #FOS: Mathematics #FOS: Physical sciences #Laser-induced spectroscopy and plasma #Mathematical Physics (math-ph) #Plasma Diagnostics and Applications #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.2504.15837

openalex publication_date 2025/04/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We introduce a variation of the classic ballistic deposition model in which vertically falling blocks can only stick to the top or the upper right corner of growing columns. We establish that the fluctuations of the height function at points near the t-axis are given by the GUE ensemble and its correspondent Tracy-Widom limiting distribution. The proof is based on a graphical construction of the process in terms of a directed Last Passage Percolation model.

Citations

• The Paquette-Zeitouni law of fractional logarithms for the GUE minor process and the Plancherel growth process
• Fluctuation Bounds for the Restricted Solid-on-Solid Model of Surface Growth
• Integrable fluctuations in the KPZ universality class
• Scaling limit of the heavy-tailed ballistic deposition model with p-sticking
• Existence of stationary ballistic deposition on the infinite lattice
• Superconcentration in surface growth
• The Brownian Castle
• On the Growth of a Ballistic Deposition Model on Finite Graphs
• On ballistic deposition process on a strip
• The directed landscape
• Fluctuation lower bounds in planar random growth models
• Proof of the path localization conjecture for directed polymers
• The KPZ fixed point
• Kardar-Parisi-Zhang Universality
• Ballistic deposition patterns beneath a growing KPZ interface
• Growth and roughness of the interface for ballistic deposition
• A GUE Central Limit Theorem and Universality of Directed First and Last Passage Site Percolation
• A universality property for last-passage percolation paths close to the axis
• Distribution functions for largest eigenvalues and their applications
• Random matrices, non-colliding processes and queues
• Transversal fluctuations for increasing subsequences on the plane
• Strong law of large numbers for the interface in ballistic deposition
• An approximation of partial sums of independent RV's, and the sample DF. II

Related

• Lower bound for large local transversal fluctuations of Geodesics in Last Passage Percolation
• Asymptotic function for multigrowth surfaces using power-law noise
• Origins of scaling corrections in ballistic growth models
• Fluctuations of the one-dimensional polynuclear growth model with external sources
• Limit shape and fluctuations for exactly solvable inhomogeneous corner growth models