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arXiv · 2608.02211

Front Selection Is Not Determined by Renormalization-Group Stability

Ko Okumura
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Abstract

The Fisher--Kolmogorov--Petrovsky--Piskunov equation provides a paradigmatic example of front propagation and asymptotic-state selection. Using a unified renormalization-group (RG) framework, we show that its traveling-wave solutions form a continuous family of RG fixed points and that all fronts with $v \ge 2$ are RG-stable. Nevertheless, the asymptotically selected front is not determined by RG stability. The FKPP equation therefore provides an explicit example in which RG fixed-point stability and asymptotic-state selection are distinct concepts.

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Ko Okumura. 2026-08-03. Front Selection Is Not Determined by Renormalization-Group Stability. https://arxiv.org/abs/2608.02211

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