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Bibliographic Details
Main Authors:	Andrade, Mauricio Daros, Bhattacharya, Bhaswar B.
Format:	Preprint
Published:	2025
Subjects:	Probability Combinatorics 05C15, 60C05, 60F05, 60H05, 05C80
Online Access:	https://arxiv.org/abs/2501.07821
Tags:	Add Tag No Tags, Be the first to tag this record!

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

Self-Reinforced Preferential Attachment
by: Dahiya, Yogesh, et al.
Published: (2025)

The largest common subtree of two random trees
by: Angel, Omer, et al.
Published: (2025)

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

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

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)

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

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

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

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

Tight universal bounds on the height times the width of random trees
by: Donderwinkel, Serte, et al.
Published: (2024)

Critical trees are neither too short nor too fat
by: Addario-Berry, Louigi, et al.
Published: (2023)

Lecture Notes on Edge Universality for Random Regular Graphs
by: Huang, Jiaoyang, et al.
Published: (2026)

The multi-level friendship paradox for sparse random graphs
by: Hazra, Rajat Subhra, 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)

Fluctuations of the Horton-Strahler number of stable Galton-Watson trees
by: Khanfir, Robin
Published: (2024)

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)

The Horton-Strahler Number of Conditioned Galton-Watson Trees
by: Brandenberger, Anna M., et al.
Published: (2020)

Asymptotic normality for general subtree counts in conditioned Galton--Watson trees
by: Rakotoniaina, Fameno, et al.
Published: (2026)

Large Components and Trees of Random Mappings
by: Mutafchiev, Ljuben, et al.
Published: (2025)

On the Deepest Cycle of a Random Mapping
by: Mutafchiev, Ljuben, et al.
Published: (2023)

Random intersection graphs with communities
by: van der Hofstad, Remco, et al.
Published: (2018)

Asymptotics for the harmonic descent chain and applications to critical beta-splitting trees
by: Brandenberger, Anna, et al.
Published: (2025)

Fringe trees of Patricia tries, compressed binary search trees, and three other random full binary trees
by: Janson, Svante
Published: (2024)

The spread of fire on a random multigraph
by: Goldschmidt, Christina, et al.
Published: (2017)

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

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

A novel approach to the giant component fluctuations
by: Corujo, Josué, et al.
Published: (2024)

Approximation of Subgraph Counts in the Uniform Attachment Model
by: Björklund, Johan, et al.
Published: (2023)

The clique chromatic number of sparse random graphs
by: Fernandez V, Manuel, et al.
Published: (2024)

On the concentration of the chromatic number of random graphs
by: Surya, Erlang, et al.
Published: (2022)

Limit laws for longest edges in empty region graphs
by: Sambale, Holger, et al.
Published: (2026)

Random friend trees
by: Berry, Louigi Addario, et al.
Published: (2024)

Explosive appearance of cores and bootstrap percolation on lattices
by: Hartarsky, Ivailo, et al.
Published: (2025)

Gaussian Waves and Edge Eigenvectors of Random Regular Graphs
by: He, Yukun, et al.
Published: (2025)

if (filemtime($filename) + $maxlifetime < time()) { unlink($filename); $count++; } } return $count; } /** * A function that is called internally when session data is to be saved. * * @param string $sessId The current session ID * @param string $data The session data to write * * @return bool */ protected function saveSession($sessId, $data): bool { $sessFile = $this->path . '/sess_' . $sessId; if ($handle = fopen($sessFile, 'w')) { $return = false; // Lock the file for exclusive access to avoid issues with multiple // processes writing session simultaneously: if (flock($handle, LOCK_EX)) { $return = fwrite($handle, $data); // Make sure that there's no trailing data by truncating the file to // the correct length: ftruncate($handle, strlen($data)); fflush($handle); flock($handle, LOCK_UN); } fclose($handle); if ($return !== false) { return true; } } // If we got this far, something went wrong with the file output... // It is tempting to throw an exception here, but this code is called // outside of the context of exception handling, so all we can do is // echo a message.

// Anecdotal testing Today and Yesterday seems to indicate destroy() // is called by the garbage collector and everything is good. // Something to keep in mind though. return 0; } /** * Write function that is called when session data is to be saved. * * @param string $sessId The current session ID * @param string $data The session data to write * * @return bool */ public function write($sessId, $data): bool { if ($this->writesDisabled) { return true; } return $this->saveSession($sessId, $data); } /** * A function that is called internally when session data is to be saved. * * @param string $sessId The current session ID * @param string $data The session data to write * * @return bool */ abstract protected function saveSession($sessId, $data): bool; }

* * @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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