2407.18052
Most probable escape paths in perturbed gradient systems
Katherine Slyman, Mackenzie Simper, John A. Gemmer, Björn Sandstede
correcthigh confidence
- Category
- math.DS
- Journal tier
- Specialist/Solid
- Processed
- Sep 28, 2025, 12:56 AM
- arXiv Links
- Abstract ↗PDF ↗
Audit review
Both the paper and the model expand the heteroclinic solutions in µ, derive identical linear first-order systems for (y1,u1,v1), use the antisymmetric part of gu to force v1 ≠ 0, and then conclude u1 − y1 ≠ 0 so that the most probable exit path differs from the time-reversed heteroclinic at order µ. The paper adds rigor via exponential dichotomies and a Fredholm solvability check; the model explicitly carries out the final lower-bound step sup |y*−u*| ≥ δ|µ|. Aside from that minor presentational difference, the arguments are essentially the same.
Referee report (LaTeX)
\textbf{Recommendation:} minor revisions
\textbf{Journal Tier:} specialist/solid
\textbf{Justification:}
The work gives a crisp, verifiable criterion for when the most probable escape path ceases to coincide with the time-reversed heteroclinic under non-symmetric perturbations of a gradient system. The method avoids quasipotential computation, relying instead on Euler–Lagrange dynamics and a clean first-order analysis backed by exponential dichotomy/Fredholm theory. The contribution is technically solid and well supported by a didactic example; minor presentational edits would make the argument fully transparent.