Scaling and local limits of Baxter permutations and bipolar orientations through coalescent-walk processes

DOI10.1214/21-AOP1559zbMath1504.60163arXiv2008.09086OpenAlexW3071841790MaRDI QIDQ2139103

Jacopo Borga, Mickaël Maazoun

Publication date: 17 May 2022

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2008.09086

zbMATH Keywords

permutationsplanar mapslocal and scaling limitswalks in cones

Mathematics Subject Classification ID

Permutations, words, matrices (05A05) Combinatorial probability (60C05) Stochastic (Schramm-)Loewner evolution (SLE) (60J67) Coalescent processes (60J90)

Related Items (6)

The runsort permuton ⋮ The skew Brownian permuton: A new universality class for random constrained permutations ⋮ On the enumeration of plane bipolar posets and transversal structures ⋮ Baxter permuton and Liouville quantum gravity ⋮ Power-law bounds for increasing subsequences in Brownian separable permutons and homogeneous sets in Brownian cographons ⋮ The permuton limit of strong-Baxter and semi-Baxter permutations is the skew Brownian permuton

Cites Work

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• Uniqueness and universality of the Brownian map
• The Brownian map is the scaling limit of uniform random plane quadrangulations
• The solution of the perturbed Tanaka-equation is pathwise unique
• The shape of random pattern-avoiding permutations
• Enumeration schemes for vincular patterns
• Large deviations for permutations avoiding monotone patterns
• Baxter permutations and plane bipolar orientations
• A decorated tree approach to random permutations in substitution-closed classes
• A mating-of-trees approach for graph distances in random planar maps
• On the constructions of the skew Brownian motion
• Baxter permutations rise again
• The number of Baxter permutations
• Four classes of pattern-avoiding permutations under one roof: Generating trees with two labels
• The Brownian limit of separable permutations
• Lenses in skew Brownian flow
• Flows, coalescence and noise.
• Limits of permutation sequences
• Almost square permutations are typically square
• Invariance principles for random walks in cones
• Universal limits of substitution-closed permutation classes
• Local convergence for permutations and local limits for uniform \(\rho \)-avoiding permutations with \(|\rho |=3\)
• Liouville quantum gravity spheres as matings of finite-diameter trees
• Random walks in cones
• Bipolar orientations on planar maps and \(\mathrm{SLE}_{12}\)
• Enumerating five families of pattern-avoiding inversion sequences; and introducing the powered Catalan numbers
• Generating trees for permutations avoiding generalized patterns
• Schnyder decompositions for regular plane graphs and application to drawing
• Bijections for Baxter families and related objects
• Square permutations are typically rectangular
• Random Measures, Theory and Applications
• Semi-Baxter and Strong-Baxter: Two Relatives of the Baxter Sequence
• Fixed points of 321-avoiding permutations
• On the Brownian separable permuton
• Permutations with fixed pattern densities
• On Fixed Points of the Composite of Commuting Functions
• The Expected Shape of Random Doubly Alternating Baxter Permutations
• Pattern‐avoiding permutations and Brownian excursion part I: Shapes and fluctuations
• Asymptotic normality of consecutive patterns in permutations encoded by generating trees with one‐dimensional labels

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