Research output: Contribution to journal › Article › peer-review
Sandpile Solitons via Smoothing of Superharmonic Functions. / Kalinin, Nikita; Shkolnikov, Mikhail.
In: Communications in Mathematical Physics, Vol. 378, No. 3, 01.09.2020, p. 1649-1675.Research output: Contribution to journal › Article › peer-review
}
TY - JOUR
T1 - Sandpile Solitons via Smoothing of Superharmonic Functions
AU - Kalinin, Nikita
AU - Shkolnikov, Mikhail
PY - 2020/9/1
Y1 - 2020/9/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85089480499&partnerID=8YFLogxK
U2 - 10.1007/s00220-020-03828-8
DO - 10.1007/s00220-020-03828-8
M3 - Article
AN - SCOPUS:85089480499
VL - 378
SP - 1649
EP - 1675
JO - Communications in Mathematical Physics
JF - Communications in Mathematical Physics
SN - 0010-3616
IS - 3
ER -
ID: 62717194