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Bibliographic Details
Main Authors:	Alves, Caio, Teixeira, Augusto
Format:	Preprint
Published:	2021
Subjects:	Probability 60K35, 82B43
Online Access:	https://arxiv.org/abs/2112.10055
Tags:	Add Tag No Tags, Be the first to tag this record!

Convergence of $k$-point functions in high dimensional percolation
by: Chatterjee, Shirshendu, et al.
Published: (2026)

Exploring the phase transition of planar FK-percolation
by: Manolescu, Ioan
Published: (2025)

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

Non-coincidence of critical points for directed polymers on supercritical percolation clusters
by: Cottini, Francesca, et al.
Published: (2025)

Spectral dimensions for one-dimensional critical long-range percolation
by: Fan, Zherui, et al.
Published: (2025)

Uniqueness and dimension for the geodesic of the critical long-range percolation metric
by: Ding, Jian, et al.
Published: (2025)

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

Truncation of long-range percolation with non-summable interactions in dimensions $d\geq 3$
by: Bäumler, Johannes
Published: (2024)

The polynomial growth of effective resistances in one-dimensional critical long-range percolation
by: Ding, Jian, et al.
Published: (2025)

Polynomial lower bound on the effective resistance for the one-dimensional critical long-range percolation
by: Ding, Jian, et al.
Published: (2024)

High-intensity Voronoi percolation on manifolds
by: Bühler, Tillmann, et al.
Published: (2025)

Hyperbolic site percolation
by: Grimmett, Geoffrey R., et al.
Published: (2022)

Asymptotics for the percolation threshold of finitary random interlacements in four and higher dimensions
by: Bi, Yijie, et al.
Published: (2025)

Supercritical sharpness for Voronoi percolation
by: Dembin, Barbara, et al.
Published: (2023)

An upper bound on geodesic length in 2D critical first-passage percolation
by: Bates, Erik, et al.
Published: (2023)

Sharpness of the percolation phase transition for weighted random connection models
by: Caicedo, Alejandro, et al.
Published: (2025)

Anisotropic non-oriented bond percolation in high dimensions
by: Gomes, Pablo A., et al.
Published: (2021)

Solidification estimates for random walks on supercritical percolation clusters
by: Chiarini, Alberto, et al.
Published: (2025)

Isoperimetric lower bounds for critical exponents for long-range percolation
by: Bäumler, Johannes, et al.
Published: (2022)

Absence of weak disorder for directed polymers on supercritical percolation clusters
by: Nitzschner, Maximilian
Published: (2022)

Limiting distribution of the chemical distance in high dimensional critical percolation
by: Chatterjee, Shirshendu, et al.
Published: (2025)

Uniform analyticity of local observables in FK-percolation and analyticity of the Ising spontaneous magnetisation
by: D'Alimonte, Lucas, et al.
Published: (2026)

Robust construction of the incipient infinite cluster in high dimensional critical percolation
by: Chatterjee, Shirshendu, et al.
Published: (2025)

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

An alternative approach for the mean-field behaviour of spread-out Bernoulli percolation in dimensions $d>6$
by: Duminil-Copin, Hugo, et al.
Published: (2024)

First passage percolation with long-range correlations and applications to random Schrödinger operators
by: Andres, Sebastian, et al.
Published: (2021)

Comparison of arm exponents in planar FK-percolation
by: Gassmann, Loïc, et al.
Published: (2024)

The polynomial growth of the infinite long-range percolation cluster
by: Bäumler, Johannes
Published: (2023)

One-arm exponents of high-dimensional percolation revisited
by: van Engelenburg, Diederik, et al.
Published: (2025)

Decay of connection probability in high-dimensional continuum percolation
by: Dickson, Matthew, et al.
Published: (2025)

Superconcentration and chaos in Bernoulli percolation
by: Nguyen, Van Quyet
Published: (2026)

Quenched local limit theorem for a directed random walk on the backbone of a supercritical oriented percolation cluster for $d \ge 1$
by: Bethuelsen, Stein Andreas, et al.
Published: (2024)

Subdiffusive concentration for the chemical distance in Bernoulli percolation
by: Can, Van Hao, et al.
Published: (2024)

Crossover from subcritical to critical decay: random walk, self-avoiding walk, percolation
by: Liu, Yucheng, et al.
Published: (2026)

Behavior of the distance exponent for $\frac{1}{|x-y|^{2d}}$ long-range percolation
by: Bäumler, Johannes
Published: (2022)

Upper bounds for critical probabilities in Bernoulli Percolation models
by: Gomes, Pablo A., et al.
Published: (2021)

Bi-infinite incipient cluster in high dimensions
by: Cabezas, Manuel, et al.
Published: (2025)

The extinction of the contact process in a one-dimensional random environment with long-range interactions
by: Gomes, Pablo A., et al.
Published: (2025)

The Poisson stick model in hyperbolic space
by: Broman, Erik I., et al.
Published: (2025)

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// 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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