Moderate deviations of suprema of Gaussian processes A cyclic approximation criterion

Fuente: arXiv

Saved in:

Bibliographic Details
Main Author:	Weber, Michel
Format:	Preprint
Published:	2025
Subjects:	Probability 42A38, 60G50
Online Access:	Acceder al recurso
Tags:	Add Tag No Tags, Be the first to tag this record!

Distributional stability of the Szarek and Ball inequalities
by: Eskenazis, Alexandros, et al.
Published: (2023)

Persistence and Ball Exponents for Gaussian Stationary Processes
by: Feldheim, Naomi, et al.
Published: (2021)

Bounding suprema of canonical processes via convex hull
by: Latała, Rafał
Published: (2022)

Elephants explore in spirals sometimes
by: Laulin, Lucile, et al.
Published: (2025)

Random walks and quadratic number fields
by: Borda, Bence
Published: (2025)

Hyperuniformity and optimal transport of point processes
by: Lachièze-Rey, Raphaël, et al.
Published: (2024)

Capacity of the range of random walk: Moderate deviations in dimensions 4 and 5
by: Adhikari, Arka, et al.
Published: (2025)

On the multidimensional elephant random walk with stops
by: Bercu, Bernard
Published: (2025)

Wasserstein Convergence Rates for Empirical Measures of Random Subsequence of $\{nα\}$
by: Wu, Bingyao, et al.
Published: (2024)

Random walks on the circle and Diophantine approximation
by: Berkes, Istvan, et al.
Published: (2022)

Beyond Wald's Equation and the Optional Sampling Theorem
by: Klass, Michael J., et al.
Published: (2026)

On multidimensional elephant random walk with stops and random step sizes
by: Ghosh, Shyan, et al.
Published: (2026)

Large deviation principle for the stationary solutions of stochastic functional differential equations with infinite delay
by: Liu, Yong, et al.
Published: (2025)

Extremal Process of Last Progeny Modified Branching Random Walks
by: Ghosh, Partha Pratim, et al.
Published: (2024)

Cotlar martingale transforms and related singular integrals
by: Bañuelos, Rodrigo
Published: (2026)

Elephant random walks on infinite Cayley trees
by: Mukherjee, Soumendu Sundar
Published: (2025)

A general correlation inequality for level sets of sums of independent random variables using the Bernoulli part with applications to the almost sure local limit theorem
by: Weber, Michel J. G.
Published: (2023)

On large deviations for the range of a two-dimensional random walk
by: Popov, Serguei, et al.
Published: (2026)

On large deviation probabilities for self-normalized sums of random variables
by: Borovkov, Konstantin
Published: (2025)

Corrected diffusion approximation for random walks conditioned to stay positive
by: Denisov, Denis, et al.
Published: (2026)

Asymptotic expansions for normal deviations of random walks conditioned to stay positive
by: Denisov, Denis, et al.
Published: (2024)

Sharp Decoupling Inequalities for the Variances and Second Moments of Sums of Dependent Random Variables
by: de la Pena, Victor H., et al.
Published: (2025)

Precise large deviations of some risk objectives related to the net loss process in two nonstandard risk models
by: Chen, Yang, et al.
Published: (2023)

Permuton limit of a generalization of the Mallows and $k$-card-minimum models
by: Jasińska, Joanna, et al.
Published: (2024)

Moderate Deviations for the Capacity of the Random Walk range in dimension four
by: Adhikari, Arka, et al.
Published: (2023)

Hyperuniformity and non-hyperuniformity of zeros of Gaussian Weyl-Heisenberg Functions
by: Feldheim, Naomi, et al.
Published: (2024)

Discrete analogues of second-order Riesz transforms
by: Bañuelos, Rodrigo, et al.
Published: (2025)

Sharp $\ell^p$ inequalities for discrete singular integrals on the lattice $\mathbb{Z}^d$
by: Bañuelos, Rodrigo, et al.
Published: (2022)

Multidimensional compound Poisson approximations for symmetric distributions
by: Čekanavičius, Vydas, et al.
Published: (2026)

Elephant random walk on the infinite dihedral group $\mathbb{Z}_2 * \mathbb{Z}_2$
by: Mukherjee, Soumendu Sundar, et al.
Published: (2026)

A uniform semi-local limit theorem along sets of multiples for sums of i.i.d. random variables
by: Weber, Michel J. G.
Published: (2022)

Some arithmetic properties of Pólya's urn
by: Fernández, José L., et al.
Published: (2021)

A Sharp Gaussian Tail Bound for Sums of Uniforms
by: He, Xinjie, et al.
Published: (2023)

Gaussian Rough Paths Lifts via Complementary Young Regularity
by: Gassiat, Paul, et al.
Published: (2023)

Cramér's moderate deviations for martingales with applications
by: Fan, Xiequan, et al.
Published: (2022)

Quenched large deviations for randomly weighted geodesic random walks
by: Versendaal, Rik
Published: (2026)

Gaussian approximation for non-linearity parameter estimation in perturbed random fields on the sphere
by: Durastanti, Claudio
Published: (2025)

Classical and Almost Sure Local Limit Theorems
by: Szewczak, Zbigniew, et al.
Published: (2022)

On Rozanov's Theorem and strenghtened asymptotic uniform distribution
by: Weber, Michel J. G.
Published: (2022)

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

Key	Value
ui	"standard"
language	"en"
VUFIND_SESSION	"e3ca309faca3e6b9f4a17b9d8ae404a3"

Session

Key	Value
__Laminas	array:2 [`"_REQUEST_ACCESS_TIME" => 1790897452.0032 "_VALID" => array:1 [ "Laminas\Session\Validator\Id" => "e3ca309faca3e6b9f4a17b9d8ae404a3" ]`]
SessionState	Laminas\Stdlib\ArrayObject {#938}
FlashMessenger	Laminas\Stdlib\ArrayObject {#1433}
SessionHelper	Laminas\Stdlib\ArrayObject {#1759}

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_COOKIE	"ui=standard; language=en; VUFIND_SESSION=e3ca309faca3e6b9f4a17b9d8ae404a3"
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	"216.73.217.142"
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	"7770"
REDIRECT_URL	""" /Record/\n arxiv_https___arxiv_org_abs_2504_11198/Similar """
GATEWAY_INTERFACE	"CGI/1.1"
SERVER_PROTOCOL	"HTTP/1.1"
REQUEST_METHOD	"GET"
QUERY_STRING	""
REQUEST_URI	"/Record/%0Aarxiv_https___arxiv_org_abs_2504_11198/Similar"
SCRIPT_NAME	"/index.php"
PHP_SELF	"/index.php"
REQUEST_TIME_FLOAT	1790897451.9918
REQUEST_TIME	1790897451

Environment Variables empty

Registered Handlers

0. Whoops\Handler\PrettyPageHandler

Environment & details:

GET Data empty

POST Data empty

Files empty

Key	Value
ui	"standard"
language	"en"
VUFIND_SESSION	"e3ca309faca3e6b9f4a17b9d8ae404a3"

Session

Key	Value
__Laminas	array:2 [`"_REQUEST_ACCESS_TIME" => 1790897452.0032 "_VALID" => array:1 [ "Laminas\Session\Validator\Id" => "e3ca309faca3e6b9f4a17b9d8ae404a3" ]`]
SessionState	Laminas\Stdlib\ArrayObject {#938}
FlashMessenger	Laminas\Stdlib\ArrayObject {#1433}
SessionHelper	Laminas\Stdlib\ArrayObject {#1759}

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_COOKIE	"ui=standard; language=en; VUFIND_SESSION=e3ca309faca3e6b9f4a17b9d8ae404a3"
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	"216.73.217.142"
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	"7770"
REDIRECT_URL	""" /Record/\n arxiv_https___arxiv_org_abs_2504_11198/Similar """
GATEWAY_INTERFACE	"CGI/1.1"
SERVER_PROTOCOL	"HTTP/1.1"
REQUEST_METHOD	"GET"
QUERY_STRING	""
REQUEST_URI	"/Record/%0Aarxiv_https___arxiv_org_abs_2504_11198/Similar"
SCRIPT_NAME	"/index.php"
PHP_SELF	"/index.php"
REQUEST_TIME_FLOAT	1790897451.9918
REQUEST_TIME	1790897451

Environment Variables empty

Registered Handlers

0. Whoops\Handler\PrettyPageHandler

Similar Items

Similar Items

Environment & details:

Environment & details: