kth.sePublications
Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
On the Domino Shuffle and Matrix Refactorizations
Department of Mathematical Sciences, Durham University, Durham, UK.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0002-7598-4521
Number of Authors: 22023 (English)In: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 401, no 2, p. 1417-1467Article in journal (Refereed) Published
Abstract [en]

This paper is motivated by computing correlations for domino tilings of the Aztec diamond. It is inspired by two of the three distinct methods that have recently been used in the simplest case of a doubly periodic weighting, that is, the two-periodic Aztec diamond. One of the methods, powered by the domino shuffle, involves inverting the Kasteleyn matrix giving correlations through the local statistics formula. Another of the methods, driven by a Wiener–Hopf factorization for two-by-two matrix-valued functions, involves the Eynard–Mehta Theorem. For arbitrary weights, the Wiener–Hopf factorization can be replaced by an LU- and UL-decomposition, based on a matrix refactorization, for the product of the transition matrices. This paper shows that, for arbitrary weightings of the Aztec diamond, the evolution of the face weights under the domino shuffle and the matrix refactorization is the same. In particular, these dynamics can be used to find the inverse of the LGV matrix in the Eynard–Mehta Theorem.

Place, publisher, year, edition, pages
Springer Nature , 2023. Vol. 401, no 2, p. 1417-1467
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:kth:diva-332965DOI: 10.1007/s00220-023-04676-yISI: 000963894800001Scopus ID: 2-s2.0-85151921139OAI: oai:DiVA.org:kth-332965DiVA, id: diva2:1783834
Note

QC 20230725

Available from: 2023-07-25 Created: 2023-07-25 Last updated: 2023-07-25Bibliographically approved

Open Access in DiVA

No full text in DiVA

Other links

Publisher's full textScopus

Authority records

Duits, Maurice

Search in DiVA

By author/editor
Duits, Maurice
By organisation
Mathematics (Div.)
In the same journal
Communications in Mathematical Physics
Probability Theory and Statistics

Search outside of DiVA

GoogleGoogle Scholar

doi
urn-nbn

Altmetric score

doi
urn-nbn
Total: 25 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf