Sandpile solitons via smoothing of superharmonic functions
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2017
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866908625458429952 |
|---|---|
| author | Kalinin, Nikita Shkolnikov, Mikhail |
| author_facet | Kalinin, Nikita Shkolnikov, Mikhail |
| contents | Let $F:\mathbb Z^2\to \mathbb Z$ be the pointwise minimum of several linear functions. The theory of smoothing of integer-valued superharmonic function allows us to prove that under certain conditions there exists the pointwise minimal superharmonic function which coincides with $F$ "at infinity".
We develop such a theory to prove the existence of so-called solitons (or strings) in a certain 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 a square where solitons appear according to experiments. We prove that sandpile states, defined using our smoothing procedure, move changeless when we send waves (that is why we call them solitons), and can interact, forming triads and nodes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1711_04285 |
| institution | arXiv |
| publishDate | 2017 |
| record_format | arxiv |
| spellingShingle | Sandpile solitons via smoothing of superharmonic functions Kalinin, Nikita Shkolnikov, Mikhail Combinatorics Dynamical Systems 37B15 37E15 05C81 05C57 14T05 Let $F:\mathbb Z^2\to \mathbb Z$ be the pointwise minimum of several linear functions. The theory of smoothing of integer-valued superharmonic function allows us to prove that under certain conditions there exists the pointwise minimal superharmonic function which coincides with $F$ "at infinity". We develop such a theory to prove the existence of so-called solitons (or strings) in a certain 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 a square where solitons appear according to experiments. We prove that sandpile states, defined using our smoothing procedure, move changeless when we send waves (that is why we call them solitons), and can interact, forming triads and nodes. |
| title | Sandpile solitons via smoothing of superharmonic functions |
| topic | Combinatorics Dynamical Systems 37B15 37E15 05C81 05C57 14T05 |
| url | https://arxiv.org/abs/1711.04285 |