Critical percolation on the discrete torus in high dimensions

Fuente: arXiv

Saved in:

Bibliographic Details
Main Authors:	Blanc-Renaudie, Arthur, Nachmias, Asaf
Format:	Preprint
Published:	2025
Subjects:	Probability
Online Access:	Acceder al recurso
Tags:	Add Tag No Tags, Be the first to tag this record!

A.S. convergence for infinite colour Pólya urns associated with stable random walks
by: Blanc-Renaudie, Arthur
Published: (2023)

Limit of trees with fixed degree sequence
by: Blanc-Renaudie, Arthur
Published: (2021)

Potentials in recurrent networks: a survey
by: Nachmias, Asaf, et al.
Published: (2025)

The wired minimal spanning forest on the Poisson-weighted infinite tree
by: Nachmias, Asaf, et al.
Published: (2022)

Local limits of determinantal processes
by: Nachmias, Asaf, et al.
Published: (2025)

Every recurrent network has a potential tending to infinity
by: Nachmias, Asaf, et al.
Published: (2025)

Scaling limit of trees with vertices of fixed degrees and heights
by: Blanc-Renaudie, Arthur, et al.
Published: (2024)

Planar Maps, Random Walks and Circle Packing
by: Nachmias, Asaf
Published: (2020)

Determinants of Laplacians on converging hyperbolic surfaces
by: Gross, Renan, et al.
Published: (2026)

Uniform attachment with freezing
by: Bellin, Étienne, et al.
Published: (2023)

A sharp lower bound on the small eigenvalues of surfaces
by: Gross, Renan, et al.
Published: (2024)

A Tight Bound on Localization of Electrical Flows
by: Gurel-Gurevich, Ori, et al.
Published: (2026)

Long-range first-passage percolation on the torus
by: van der Hofstad, Remco, et al.
Published: (2023)

Uniform attachment with freezing: Scaling limits
by: Bellin, Étienne, et al.
Published: (2023)

A phase transition for the biased tree-builder random walk
by: Blanc-Renaudie, Arthur, et al.
Published: (2024)

Asymptotic expansion of the critical point for oriented percolation in high dimensions
by: Kawamoto, Noe
Published: (2025)

Critical long-range percolation II: Low effective dimension
by: Hutchcroft, Tom
Published: (2025)

Critical long-range percolation III: The upper critical dimension
by: Hutchcroft, Tom
Published: (2025)

Critical long-range percolation I: High effective dimension
by: Hutchcroft, Tom
Published: (2025)

Critical site percolation and cutsets
by: Li, Zhongyang
Published: (2024)

Shadow and percolation I: discrete landscapes with independence
by: Vernotte, David
Published: (2025)

Shadow and percolation II: discrete and continuous landscapes with correlations
by: Vernotte, David
Published: (2025)

The longest edge in discrete and continuous long-range percolation
by: Rousselle, Arnaud, et al.
Published: (2021)

Capacity in high dimensional percolation
by: Asselah, Amine, et al.
Published: (2025)

Critical percolation on slabs with random columnar disorder
by: Castro, Matheus B., et al.
Published: (2024)

On Loops in critical high-dimensional percolation
by: Carpenter, Amelia, et al.
Published: (2025)

Local limit theorems for random walks on a large discrete torus
by: Gu, Yandong, et al.
Published: (2024)

Critical fluctuations of last passage percolation with thick boundaries
by: Emrah, Elnur, et al.
Published: (2025)

Exact values of Fourier dimensions of Gaussian multiplicative chaos on high dimensional torus
by: Chen, Yukun, et al.
Published: (2025)

Dimension jump at the uniqueness threshold for percolation in $\infty+d$ dimensions
by: Hutchcroft, Tom, et al.
Published: (2024)

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

Geometry of critical discrete structures: percolation on the hierarchical lattice
by: Sen, Sanchayan
Published: (2025)

Critical speeding-up in dynamical percolation
by: Elci, Eren Metin, et al.
Published: (2024)

On the time constant of high dimensional first passage percolation, revisited
by: Auffinger, Antonio, et al.
Published: (2025)

Critical Ising correlations on a torus
by: Bayraktaroglu, Baran, et al.
Published: (2025)

Loop percolation versus link percolation in the random loop model
by: Betz, Volker, et al.
Published: (2024)

Settlement percolation: global maps of Critical Distances
by: Schorcht, Martin, et al.
Published: (2026)

Universal behaviour of majority bootstrap percolation on high-dimensional geometric graphs
by: Collares, Maurício, et al.
Published: (2024)

Scaling limits and universality: Critical percolation on weighted graphs converging to an $L^3$ graphon
by: Baslingker, Jnaneshwar, et al.
Published: (2023)

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'

Environment & details:

GET Data empty

POST Data empty

Files empty

Cookies empty

Session

Key	Value
__Laminas	array:2 [`"_REQUEST_ACCESS_TIME" => 1790777560.3708 "_VALID" => array:1 [ "Laminas\Session\Validator\Id" => "5f225b3b1c1146996d9d538bb518764c" ]`]
SessionState	Laminas\Stdlib\ArrayObject {#937}
FlashMessenger	Laminas\Stdlib\ArrayObject {#1432}
SessionHelper	Laminas\Stdlib\ArrayObject {#1758}

Server/Request Data

Key	Value
REDIRECT_VUFIND_LOCAL_DIR	"/usr/local/vufind/local"
REDIRECT_HTTPS	"on"
REDIRECT_SSL_TLS_SNI	"info.umar.mx"
REDIRECT_STATUS	"200"
VUFIND_LOCAL_DIR	"/usr/local/vufind/local"
HTTPS	"on"
SSL_TLS_SNI	"info.umar.mx"
HTTP_ACCEPT	"/"
HTTP_USER_AGENT	"Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)"
HTTP_ACCEPT_ENCODING	"gzip, br, zstd, deflate"
HTTP_HOST	"info.umar.mx"
PATH	"/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/snap/bin"
SERVER_SIGNATURE	"<address>Apache/2.4.66 (Ubuntu) Server at info.umar.mx Port 443</address>\n"
SERVER_SOFTWARE	"Apache/2.4.66 (Ubuntu)"
SERVER_NAME	"info.umar.mx"
SERVER_ADDR	"200.23.222.19"
SERVER_PORT	"443"
REMOTE_ADDR	"216.73.216.147"
DOCUMENT_ROOT	"/usr/local/vufind/public"
REQUEST_SCHEME	"https"
CONTEXT_PREFIX	""
CONTEXT_DOCUMENT_ROOT	"/usr/local/vufind/public"
SERVER_ADMIN	"admin@localhost"
SCRIPT_FILENAME	"/usr/local/vufind/public/index.php"
REMOTE_PORT	"21713"
REDIRECT_URL	""" /Record/\n arxiv_https___arxiv_org_abs_2512_19672/Similar """
GATEWAY_INTERFACE	"CGI/1.1"
SERVER_PROTOCOL	"HTTP/1.1"
REQUEST_METHOD	"GET"
QUERY_STRING	""
REQUEST_URI	"/Record/%0Aarxiv_https___arxiv_org_abs_2512_19672/Similar"
SCRIPT_NAME	"/index.php"
PHP_SELF	"/index.php"
REQUEST_TIME_FLOAT	1790777560.3534
REQUEST_TIME	1790777560

Environment Variables empty

Registered Handlers

0. Whoops\Handler\PrettyPageHandler

Environment & details:

GET Data empty

POST Data empty

Files empty

Cookies empty

Session

Key	Value
__Laminas	array:2 [`"_REQUEST_ACCESS_TIME" => 1790777560.3708 "_VALID" => array:1 [ "Laminas\Session\Validator\Id" => "5f225b3b1c1146996d9d538bb518764c" ]`]
SessionState	Laminas\Stdlib\ArrayObject {#937}
FlashMessenger	Laminas\Stdlib\ArrayObject {#1432}
SessionHelper	Laminas\Stdlib\ArrayObject {#1758}

Server/Request Data

Key	Value
REDIRECT_VUFIND_LOCAL_DIR	"/usr/local/vufind/local"
REDIRECT_HTTPS	"on"
REDIRECT_SSL_TLS_SNI	"info.umar.mx"
REDIRECT_STATUS	"200"
VUFIND_LOCAL_DIR	"/usr/local/vufind/local"
HTTPS	"on"
SSL_TLS_SNI	"info.umar.mx"
HTTP_ACCEPT	"/"
HTTP_USER_AGENT	"Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)"
HTTP_ACCEPT_ENCODING	"gzip, br, zstd, deflate"
HTTP_HOST	"info.umar.mx"
PATH	"/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/snap/bin"
SERVER_SIGNATURE	"<address>Apache/2.4.66 (Ubuntu) Server at info.umar.mx Port 443</address>\n"
SERVER_SOFTWARE	"Apache/2.4.66 (Ubuntu)"
SERVER_NAME	"info.umar.mx"
SERVER_ADDR	"200.23.222.19"
SERVER_PORT	"443"
REMOTE_ADDR	"216.73.216.147"
DOCUMENT_ROOT	"/usr/local/vufind/public"
REQUEST_SCHEME	"https"
CONTEXT_PREFIX	""
CONTEXT_DOCUMENT_ROOT	"/usr/local/vufind/public"
SERVER_ADMIN	"admin@localhost"
SCRIPT_FILENAME	"/usr/local/vufind/public/index.php"
REMOTE_PORT	"21713"
REDIRECT_URL	""" /Record/\n arxiv_https___arxiv_org_abs_2512_19672/Similar """
GATEWAY_INTERFACE	"CGI/1.1"
SERVER_PROTOCOL	"HTTP/1.1"
REQUEST_METHOD	"GET"
QUERY_STRING	""
REQUEST_URI	"/Record/%0Aarxiv_https___arxiv_org_abs_2512_19672/Similar"
SCRIPT_NAME	"/index.php"
PHP_SELF	"/index.php"
REQUEST_TIME_FLOAT	1790777560.3534
REQUEST_TIME	1790777560

Environment Variables empty

Registered Handlers

0. Whoops\Handler\PrettyPageHandler

Similar Items

Similar Items

Environment & details:

Environment & details: