On Gibbs measures and topological solitons of exterior equivariant wave maps

Bjoern Bringmann ^[1]
1. [1] Princeton University
  
  Princeton University
  
  Estados Unidos
Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 40, Nº 3, 2024, págs. 859-900
Idioma: inglés
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Resumen
- We consider k-equivariant wave maps from the exterior spatial domain R3 ∖B(0,1) into the target S 3. This model has infinitely many topological solitons Q n,k , which are indexed by their topological degree n∈Z. For each n∈Z and k≥1, we prove the existence and invariance of a Gibbs measure supported on the homotopy class of Q n,k. As a corollary, we obtain that soliton resolution fails for random initial data. Since soliton resolution is known for initial data in the energy space, this reveals a sharp contrast between deterministic and probabilistic perspectives.