DOI

Let F: Z2→ Z be the pointwise minimum of several linear functions. The theory of smoothing allows us to prove that under certain conditions there exists the pointwise minimal function among all integer-valued superharmonic functions coinciding with F “at infinity”. We develop such a theory to prove existence of so-called solitons (or strings) in a sandpile model, studied by S. Caracciolo, G. Paoletti, and A. Sportiello. Thus we made a step towards understanding the phenomena of the identity in the sandpile group for planar domains where solitons appear according to experiments. We prove that sandpile states, defined using our smoothing procedure, move changeless when we apply the wave operator (that is why we call them solitons), and can interact, forming triads and nodes.

Язык оригиналаанглийский
Страницы (с-по)1649-1675
Число страниц27
ЖурналCommunications in Mathematical Physics
Том378
Номер выпуска3
DOI
СостояниеОпубликовано - 1 сен 2020

    Предметные области Scopus

  • Статистическая и нелинейная физика
  • Математическая физика

ID: 62717194