偏置的2×2周期阿兹特克钻石和椭圆曲线。

IF 1.5 1区数学 Q2 STATISTICS & PROBABILITY

Probability Theory and Related Fields Pub Date : 2023-01-01 Epub Date: 2023-02-14 DOI:10.1007/s00440-023-01195-8

Alexei Borodin, Maurice Duits

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引用次数: 0

摘要

我们研究了具有偏置2×2周期权函数的阿兹特克金刚石的随机多米诺骨牌，并将椭圆曲线上的线性流动与该模型相关联。我们的主要结果是相关核的二重积分公式，其中被积函数用这个流表示。对于参数的特殊选择，流是周期性的，这允许我们对相关核执行鞍点分析。在这些情况下，我们计算光滑无序（或气体）区域的局部相关性。更详细地计算了流具有周期六的特殊例子，我们证明了在这种情况下，粗糙无序区域的边界是八次代数曲线。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

<ArticleTitle xmlns:ns0="http://www.w3.org/1998/Math/MathML">Biased <ns0:math><ns0:mrow><ns0:mn>2</ns0:mn><ns0:mo>×</ns0:mo><ns0:mn>2</ns0:mn></ns0:mrow></ns0:math> periodic Aztec diamond and an elliptic curve.

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Biased 2×2 periodic Aztec diamond and an elliptic curve.

We study random domino tilings of the Aztec diamond with a biased $2 \times 2$ periodic weight function and associate a linear flow on an elliptic curve to this model. Our main result is a double integral formula for the correlation kernel, in which the integrand is expressed in terms of this flow. For special choices of parameters the flow is periodic, and this allows us to perform a saddle point analysis for the correlation kernel. In these cases we compute the local correlations in the smooth disordered (or gaseous) region. The special example in which the flow has period six is worked out in more detail, and we show that in that case the boundary of the rough disordered region is an algebraic curve of degree eight.

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来源期刊

Probability Theory and Related Fields 数学-统计学与概率论

CiteScore

3.70

自引率

5.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Probability Theory and Related Fields publishes research papers in modern probability theory and its various fields of application. Thus, subjects of interest include: mathematical statistical physics, mathematical statistics, mathematical biology, theoretical computer science, and applications of probability theory to other areas of mathematics such as combinatorics, analysis, ergodic theory and geometry. Survey papers on emerging areas of importance may be considered for publication. The main languages of publication are English, French and German.