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Bibliographic Details
Main Authors:	Huang, Jiaoyang, Yau, Horng-Tzer
Format:	Preprint
Published:	2026
Subjects:	Probability Mathematical Physics Combinatorics 60B20, 05C80, 05C48, 60F05
Online Access:	https://arxiv.org/abs/2602.00975
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Gaussian Waves and Edge Eigenvectors of Random Regular Graphs
by: He, Yukun, et al.
Published: (2025)

Spectrum of Random $d$-regular Graphs Up to the Edge
by: Huang, Jiaoyang, et al.
Published: (2021)

Optimal Eigenvalue Rigidity of Random Regular Graphs
by: Huang, Jiaoyang, et al.
Published: (2024)

Geometry of Random Cayley Graphs of Abelian Groups
by: Hermon, Jonathan, et al.
Published: (2021)

Two-Point Concentration of the Domination Number of Random Graphs
by: Bohman, Tom, et al.
Published: (2024)

Semicircle laws with combined variance for non-uniform Erdős-Rényi hypergraphs
by: Avena, Luca, et al.
Published: (2026)

Extremal eigenvectors of sparse random matrices
by: He, Yukun, et al.
Published: (2025)

A Random Graph Growth Model
by: Farber, Michael, et al.
Published: (2023)

Monochromatic Subgraphs in Randomly Colored Dense Multiplex Networks
by: Andrade, Mauricio Daros, et al.
Published: (2025)

Central limit theorems for high dimensional lattice polytopes: symmetric edge polytopes
by: Donzelmann, Torben, et al.
Published: (2026)

Critical level-set percolation on finite graphs and spectral gap
by: Goswami, Subhajit, et al.
Published: (2026)

Sharp Square Root Bounds for Edge Eigenvector Universality in Sparse Random Regular Graphs
by: Nagel, Leonhard
Published: (2025)

Quantitative Edge Eigenvector Universality for Random Regular Graphs: Berry-Esseen Bounds with Explicit Constants
by: Nagel, Leonhard
Published: (2025)

Limit theorems for walks and triangles on Erdös-Rényi random graphs with large interaction radius
by: Khorunzhiy, O.
Published: (2024)

Isomorphisms between dense random graphs
by: Surya, Erlang, et al.
Published: (2023)

The rank of sparse random matrices
by: Coja-Oghlan, Amin, et al.
Published: (2019)

Edge universality of sparse Erdős-Rényi digraphs
by: He, Yukun
Published: (2023)

Central limit theorems for high dimensional lattice polytopes: cosmological polytopes
by: Donzelmann, Torben, et al.
Published: (2026)

A large deviation principle for block models
by: Borgs, Christian, et al.
Published: (2020)

Upper tail bounds for irregular graphs
by: Basak, Anirban, et al.
Published: (2025)

On the upper tail of star counts in random graphs
by: Akhmejanova, Margarita, et al.
Published: (2025)

Graph connectivity with fixed endpoints in the random-connection model
by: Liu, Qingwei, et al.
Published: (2023)

A Galton-Watson tree approach to local limits of permutations avoiding a pattern of length three
by: Park, Jungeun, et al.
Published: (2024)

Local limit theorem for joint subgraph counts
by: Sah, Ashwin, et al.
Published: (2024)

Universality of global asymptotics of Jack-deformed random Young diagrams at varying temperatures
by: Cuenca, Cesar, et al.
Published: (2023)

Upper tails of subgraph counts in directed random graphs
by: Park, Jiyun
Published: (2024)

Typical structure of sparse exponential random graph models
by: Cook, Nicholas A., et al.
Published: (2022)

Semilocalization for inhomogeneous random graphs
by: Buc-d'Alché, Thomas, et al.
Published: (2026)

Maximising homomorphism counts between digraphs
by: Lüchtrath, Lukas, et al.
Published: (2026)

Domino Tilings of the Aztec Diamond in Random Environment and Schur Generating Functions
by: Bufetov, Alexey, et al.
Published: (2025)

A short proof of a central limit theorem for the order of the giant component and $k$-core
by: Anastos, Michael, et al.
Published: (2025)

What is The Probability That A Random Graph With A Given Degree Sequence is Connected?
by: Addario-Berry, Louigi, et al.
Published: (2026)

Asymptotic size of the Karp-Sipser Core in Configuration Model
by: Chatterjee, Arnab, et al.
Published: (2025)

The asymptotic rank of adjacency matrices of weighted configuration models over arbitrary fields
by: van der Hofstad, Remco, et al.
Published: (2025)

The law of the circumference of sparse binomial random graphs
by: Anastos, Michael, et al.
Published: (2025)

A tail bound for cumulant series for complex functions of independent random variables
by: Isaev, Mikhail
Published: (2025)

Normal approximation for number of edges in random intersection graphs
by: Rybarczyk, Katarzyna, et al.
Published: (2025)

Normal approximation for subgraph count in random hypergraphs
by: Michalczuk, Wojciech, et al.
Published: (2024)

The Gaussian Wave for Graphs of Finite Cone Type
by: Dembo, Amir, et al.
Published: (2026)

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* * @return void */ public function writeClose() { // The assumption is that we're using PHP's ext/session. // session_write_close() will actually overwrite $_SESSION with an // empty array on completion -- which leads to a mismatch between what // is in the storage object and $_SESSION. To get around this, we // temporarily reset $_SESSION to an array, and then re-link it to // the storage object. // // Additionally, while you _can_ write to $_SESSION following a // session_write_close() operation, no changes made to it will be // flushed to the session handler. As such, we now mark the storage // object isImmutable. $storage = $this->getStorage(); if (! $storage->isImmutable()) { $_SESSION = $storage->toArray(true); session_write_close(); $storage->fromArray($_SESSION); $storage->markImmutable(); } } /** * Attempt to set the session name * * If the session has already been started, or if the name provided fails * validation, an exception will be raised. * * @param string $name * @return SessionManager * @throws Exception\InvalidArgumentException */ public function setName($name) { if ($this->sessionExists()) { throw new Exception\InvalidArgumentException( 'Cannot set session name after a session has already started'

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