Claudio Landim

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math.PR2025

The Gamma Expansion of the Level Two Large Deviation Rate Functional for Reversible Diffusion Processes

Claudio Landim, Jungkyoung Lee, Mauro Mariani

Fix a smooth Morse function $U : R^{d} \to R$ with finitely many critical points, and consider the solution of the stochastic differential equation \[ d\boldsym…

math.PR2025

From one-dimensional diffusion processes metastable behaviour to parabolic equations asymptotics

Claudio Landim, Christian Maura

Consider the one-dimensional elliptic operator given by \begin{equation*} (L_Îµf)(x) \;=\; b (x) \, f'(x) \,+\, Îµ\, a (x)\, f''(x) \;, \end{equation*} where the drift $b\colon R \…

math.PR2025

Metastability and time scales for parabolic equations with drift 2: the general time scale

Claudio Landim, Jungkyoung Lee, Insuk Seo

Consider the elliptic operator given by \[ \mathscr{L}_Îµf=b\cdot\nabla f+ÎµÎf \] for some smooth vector field $b : R^{d} \to R^{d}$ and $I^µ > 0$ , and the initial-valued p…

math.PR2025

$I^$ -expansion of the measure-current large deviations rate functional of non-reversible finite-state Markov chains

Seonwoo Kim, Claudio Landim

Consider a sequence of continuous-time Markov chains $(X_{t}^{(n)} : t \geq 0)$ evolving on a fixed finite state space $V$ . Let $I_{n}$ be the measure-current large deviations rate functio…

math.PR2024

Metastability and time scales for parabolic equations with drift 1: the first time scale

Claudio Landim, Jungkyoung Lee, Insuk Seo

Consider the elliptic operator given by $L_{I^} µ f = b \cdot \nabla f + I^µ I^ f$ for some smooth vector field $b : R^{d} \to R^{d}$ and a small parameter $…

The Gamma Expansion of the Level Two Large Deviation Rate Functional for Reversible Diffusion Processes

From one-dimensional diffusion processes metastable behaviour to parabolic equations asymptotics

Metastability and time scales for parabolic equations with drift 2: the general time scale

I^-expansion of the measure-current large deviations rate functional of non-reversible finite-state Markov chains

Metastability and time scales for parabolic equations with drift 1: the first time scale

$I^$ -expansion of the measure-current large deviations rate functional of non-reversible finite-state Markov chains