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Bibliographic Details
Main Author:	Morfe, Peter S.
Format:	Preprint
Published:	2025
Subjects:	Probability Analysis of PDEs
Online Access:	https://arxiv.org/abs/2511.11036
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A Critical Drift-Diffusion Equation: Intermittent Behavior via Geometric Brownian Motion on $ \textbf{SL}(n)$
by: Morfe, Peter S., et al.
Published: (2025)

A Critical Drift-Diffusion Equation: Connections to the Diffusion on $\textbf{SL}(2)$
by: Morfe, Peter, et al.
Published: (2024)

Comparison Principles for the Finsler Infinity Laplacian with Applications to Minimal Lipschitz Extensions
by: Morfe, Peter S.
Published: (2024)

The Gaussian free-field as a stream function: asymptotics of effective diffusivity in infra-red cut-off
by: Chatzigeorgiou, Georgiana, et al.
Published: (2022)

Strong existence and uniqueness for a class of quasilinear stochastic evolution equations
by: Bechtel, Sebastian, et al.
Published: (2026)

Periodic nonlinear Schrödinger equation with distributional potential and invariant measures
by: Debussche, Arnaud, et al.
Published: (2024)

Quantifying the effect of noise perturbation for the stochastic Burgers equation with additive trace-class noise
by: Cox, Sonja, et al.
Published: (2026)

Weak error estimates of Galerkin approximations for the stochastic Burgers equation driven by additive trace-class noise
by: Bréhier, Charles-Edouard, et al.
Published: (2024)

KPZ equation from a class of nonlinear SPDEs in infinite volume
by: Yang, Kevin
Published: (2025)

Gradient flow structure, well-posedness and asymptotic behavior of Fokker-Planck equation on locally finite graphs
by: Wang, Cong
Published: (2025)

Diffuse Interface Energies with Microscopic Heterogeneities: Homogenization and Rare Events
by: Morfe, Peter S., et al.
Published: (2024)

Tail bounds for the Dyson series of random Schrödinger equations
by: Black, Adam, et al.
Published: (2025)

Bogoliubov type recursions for renormalisation in regularity structures
by: Bruned, Yvain, et al.
Published: (2020)

Unique continuation on planar graphs
by: Bou-Rabee, Ahmed, et al.
Published: (2023)

The energy landscape of the Kuramoto model in random geometric graphs in a circle
by: De Vita, Cecilia, et al.
Published: (2024)

Construction of a Gibbs measure for the zonal Dirac equation
by: de Suzzoni, Anne-Sophie, et al.
Published: (2026)

Subdiffusive fractional limit of a jump-renewal equation
by: Berry, Hugues, et al.
Published: (2026)

Heat kernel asymptotics for scaling limits of isoradial graphs
by: Schwarz, Simon, et al.
Published: (2023)

Strategic geometric graphs through mean field games
by: Bertucci, Charles, et al.
Published: (2024)

An approximate solution of a case of perturbed Fokker-Planck equation
by: Luo, Yan, et al.
Published: (2025)

Asymptotic decomposition of solutions to parabolic equations with a random microstructure
by: Kleptsyna, Marina, et al.
Published: (2020)

Kolmogorov equations on the space of probability measures associated to the nonlinear filtering equation: the viscosity approach
by: Martini, Mattia
Published: (2022)

Gaussian upper bounds, volume doubling and Sobolev inequalities on graphs
by: Keller, Matthias, et al.
Published: (2024)

Delay rough evolution equations
by: Qu, Shiduo, et al.
Published: (2024)

Quasi-generalised KPZ equation
by: Bruned, Yvain, et al.
Published: (2024)

Anderson stochastic quantization equation
by: Eulry, Hugo, et al.
Published: (2024)

A game-theoretical interpretation for a doubly nonlinear parabolic equation
by: del Teso, Felix, et al.
Published: (2026)

Off-diagonal upper heat kernel bounds on graphs with unbounded geometry
by: Rose, Christian
Published: (2025)

Gaussian upper heat kernel bounds and Faber-Krahn inequalities on graphs
by: Rose, Christian
Published: (2024)

On the effect of randomization on supercritical heat equations
by: Luongo, Eliseo
Published: (2025)

Compressible Euler equations with transport noise
by: Boadi, Richard, et al.
Published: (2025)

Weak uniqueness for singular stochastic equations
by: Butkovsky, Oleg, et al.
Published: (2024)

Exciting games and Monge-Ampère equations
by: Backhoff, Julio, et al.
Published: (2024)

Non-local Boundary Value Problems, stochastic resetting and Brownian motions on graphs
by: Bonaccorsi, Stefano, et al.
Published: (2022)

Ergodicity for the fractional Magneto-Hydrodynamic equations driven by a degenerate pure jump noise
by: Wang, Xue, et al.
Published: (2025)

The small mass limit for a McKean-Vlasov equation with state-dependent friction
by: Shi, Chungang, et al.
Published: (2024)

The superposition principle for the continuity equation with singular flux
by: Almi, Stefano, et al.
Published: (2025)

On some stochastic hyperbolic equations with symplectic characteristics
by: Bernardi, Enrico, et al.
Published: (2024)

Global pathwise solutions of an abstract stochastic equation
by: Lin, Y. -X., et al.
Published: (2024)

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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