2009.05582
Network experiment demonstrates converse symmetry breaking
Ferenc Molnar, Takashi Nishikawa, Adilson E. Motter
correctmedium confidence
- Category
- math.DS
- Journal tier
- Strong Field
- Processed
- Sep 28, 2025, 12:55 AM
- arXiv Links
- Abstract ↗PDF ↗
Audit review
The paper establishes explicit stability thresholds for two noise models—discrete impulse and Ornstein–Uhlenbeck—and proves that if λmax(β*) < min{0, λmax(β̃)}, then there exist noise intensities for which the splay state is stable under β* but not under β̃. The candidate solution reproduces the same threshold-based argument, selecting a θ between the two λmax values and choosing the noise intensity (M or σ) to make λmax_th = θ, thereby matching the paper’s logic and conclusions.
Referee report (LaTeX)
\textbf{Recommendation:} minor revisions
\textbf{Journal Tier:} strong field
\textbf{Justification:}
The paper’s derivations of noise-dependent stability thresholds and their use to formulate and verify converse symmetry breaking are correct, clear, and experimentally relevant. The logic is rigorous and grounded in standard linearization and stochastic process theory. Minor improvements could further clarify parameter domains and the mapping from noise intensity to threshold values.