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Bibliographic Details
Main Author:	Durrett, Rick
Format:	Preprint
Published:	2024
Subjects:	Probability 60K35
Online Access:	https://arxiv.org/abs/2403.18592
Tags:	Add Tag No Tags, Be the first to tag this record!

First contact percolation
by: Jahnel, Benedikt, et al.
Published: (2024)

Long-range contact process and percolation on a random lattice
by: Gomes, Pablo A., et al.
Published: (2021)

Permutation invariance in last-passage percolation and the distribution of the Busemann process
by: Bates, Erik, et al.
Published: (2025)

Oriented bond-site percolation in random environment and contact processes with periodic recovery
by: Jahnel, Benedikt, et al.
Published: (2025)

Multitype contact process with sterile states
by: Lanchier, Nicolas, et al.
Published: (2025)

On the extinction phase of the contact process with an asymptomatic state
by: Lanchier, Nicolas
Published: (2025)

Biased random walk on dynamical percolation
by: Andres, Sebastian, et al.
Published: (2023)

On the intersection of critical percolation clusters and other tree-like random graphs
by: Asselah, Amine, et al.
Published: (2024)

Richardson's model and the contact process with stirring: long time behavior
by: Marchand, Régine, et al.
Published: (2025)

Biased random walk on the critical curve of dynamical percolation
by: Olzhabayev, Assylbek, et al.
Published: (2025)

Majority bootstrap percolation on the permutahedron and other high-dimensional graphs
by: Collares, Maurício, et al.
Published: (2025)

Survival of one dimensional renewal contact process
by: Santos, Rafael, et al.
Published: (2023)

The contact process with an asymptomatic state
by: Belhadji, Lamia, et al.
Published: (2023)

Random walk on dynamical percolation in Euclidean lattices: separating critical and supercritical regimes
by: Gu, Chenlin, et al.
Published: (2024)

Coupling between Brownian motion and random walks on the infinite percolation cluster
by: Gu, Chenlin, et al.
Published: (2024)

From stability to chaos in last-passage percolation
by: Ahlberg, Daniel, et al.
Published: (2023)

Coupling derivation of optimal-order central moment bounds in exponential last-passage percolation
by: Emrah, Elnur, et al.
Published: (2022)

Convex order and faster transmission in first contact percolation
by: Jahnel, Benedikt, et al.
Published: (2026)

Results on the contact process with dynamic edges or under renewals
by: Hilário, Marcelo, et al.
Published: (2021)

A note on the phase transition for independent alignment percolation
by: Hilário, Marcelo, et al.
Published: (2020)

Chaos, concentration and multiple valleys in first-passage percolation
by: Ahlberg, Daniel, et al.
Published: (2023)

The averaging process on infinite graphs
by: Gantert, Nina, et al.
Published: (2024)

$L^2$-cutoff for the averaging process on random regular graphs
by: Caputo, Pietro, et al.
Published: (2026)

Lower bounds on non-random fluctuations in planar first passage percolation
by: Hassler, Malte
Published: (2025)

A scaling limit of crossing probabilities for critical percolation on the square lattice
by: Zhang, Yu
Published: (2022)

1+O(1) asymptotics for loop percolation in five and higher dimensions
by: Vogel, Quirin
Published: (2025)

Widths of crossings in Poisson Boolean percolation
by: Manolescu, Ioan, et al.
Published: (2022)

Sensitive bootstrap percolation second term
by: Hartarsky, Ivailo
Published: (2023)

A note on last passage percolation and Schur processes
by: Dimitrov, Evgeni, et al.
Published: (2025)

The truncation property and continuity for the long-range contact process on $\mathbb{Z}^d$
by: Bethuelsen, Stein Andreas, et al.
Published: (2026)

The contact process with fitness on random trees
by: Cardona-Tobón, Natalia, et al.
Published: (2021)

Existence of subcritical percolation phases for generalised weight-dependent random connection models
by: Jahnel, Benedikt, et al.
Published: (2023)

Detection, coverage and percolation in dynamic Boolean models with random radii based on $α$-stable processes
by: Gracar, Peter, et al.
Published: (2026)

Cluster-size decay in supercritical long-range percolation
by: Jorritsma, Joost, et al.
Published: (2023)

The critical curve of long-range percolation on oriented trees
by: Couronné, Olivier, et al.
Published: (2025)

Differentiability of limit shapes in continuous first passage percolation models
by: Bakhtin, Yuri, et al.
Published: (2024)

The diffusivity of supercritical Bernoulli percolation is infinitely differentiable
by: Gu, Chenlin, et al.
Published: (2025)

Large deviations of geodesic midpoint fluctuations in last-passage percolation with general i.i.d. weights
by: Alberts, Tom, et al.
Published: (2025)

Non-equilibrium coagulation processes and subcritical percolation on evolving networks
by: Banerjee, Sayan, 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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