用三角形O(n)环模型装饰的临界玻尔兹曼平面地图的探测过程

IF 0.6 4区 数学 Q4 STATISTICS & PROBABILITY Alea-Latin American Journal of Probability and Mathematical Statistics Pub Date : 2021-12-21 DOI:10.30757/alea.v19-58
Aleksandra Korzhenkova
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引用次数: 0

摘要

在本文中,我们研究了具有仅穿过内三角面的环的尖$(\mathbf{q},g,n)$-Boltzmann环装饰映射。通过对arXiv:1809012012的剥离探索,我们证明了它在非一般临界阶段的定律可以通过一个新的特定边界条件用限制在正整数范围内的随机游动来编码。在我们认为是真的技术假设下,将这一观察结果与剥离定律的显式量相结合,我们导出了所谓嵌套统计分布的大偏差性质,并表明勘探过程与二分图上的刚性环模型具有完全相同的标度极限,二分图是arXiv:1809.2012中引入的一个特定的自相似马尔可夫过程。此外,我们通过证明arXiv:12025521论点中的缺失方向,得出了所谓不动点方程所涉及的容许权序列的等价性。
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The exploration process of critical Boltzmann planar maps decorated by a triangular O(n) loop model
In this paper we investigate pointed $(\mathbf{q}, g, n)$-Boltzmann loop-decorated maps with loops traversing only inner triangular faces. Using the peeling exploration of arXiv:1809.02012 modified to this setting we show that its law in the non-generic critical phase can be coded in terms of a random walk confined to the positive integers by a new specific boundary condition. Under a technical assumption that we believe to be true, combining this observation with explicit quantities for the peeling law we derive the large deviations property for the distribution of the so-called nesting statistic and show that the exploration process possesses exactly the same scaling limit as in the rigid loop model on bipartite maps that is a specific self-similar Markov process introduced in arXiv:1809.02012. Besides, we conclude the equivalence of the admissible weight sequences related by the so-called fixed point equation by proving the missing direction in the argument of arXiv:1202.5521.
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来源期刊
CiteScore
1.10
自引率
0.00%
发文量
48
期刊介绍: ALEA publishes research articles in probability theory, stochastic processes, mathematical statistics, and their applications. It publishes also review articles of subjects which developed considerably in recent years. All articles submitted go through a rigorous refereeing process by peers and are published immediately after accepted. ALEA is an electronic journal of the Latin-american probability and statistical community which provides open access to all of its content and uses only free programs. Authors are allowed to deposit their published article into their institutional repository, freely and with no embargo, as long as they acknowledge the source of the paper. ALEA is affiliated with the Institute of Mathematical Statistics.
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