This paper investigates the small-noise behavior (as noise parameter σ approaches zero) of exit times from the domains of attraction of various potentials, V and F. Notably, the authors apply weak assumptions to these potentials and the domain G, avoiding typical restrictions such as convexity or concavity. A key finding is the establishment of the Large Deviation Principle (LDP) for self-interacting diffusion processes initialized with generalized conditions, revealing insights into Kramers' law related to exit times and locations of diffusion within complex landscapes.
The focus of our research is the small-noise behavior of exit-time from the potentials' domain of attraction, particularly under weak assumptions about those potentials.
We establish the Large Deviation Principle for Self-interacting diffusion with generalized initial conditions, offering a significant extension of existing methods in this field.
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