三叶映射参数的渐近分布与线性λ项
Asymptotic Distribution of Parameters in Trivalent Maps and Linear Lambda Terms
摘要：
大型随机映射和随机项的结构性质可以通过研究各种感兴趣的参数的极限分布来收集。在我们的工作中，我们专注于限制类的地图和他们的对应物在Escherida演算，最近建立在这两个域之间的双射连接。在这种情况下，映射中的参数自然地对应于非参数项中的参数，反之亦然。通过一个相互作用的项和地图，我们得到各种组合规范，使我们能够访问分布的相关参数对，如：根三价映射中的桥数、闭线性二阶项中的子项数、（1，3）-叶映射中的1度顶点数、开线性二阶项中的自由变元数等。我们介绍适当的工具：一个微分方程的矩泵模式和一个由本德定理启发的组合模式。
英文摘要：
Structural properties of large random maps and lambda-terms may be gleaned by studying the limit distributions of various parameters of interest. In our work we focus on restricted classes of maps and their counterparts in the lambda-calculus, building on recent bijective connections between these two domains. In such cases, parameters in maps naturally correspond to parameters in lambda-terms and vice versa. By an interplay between lambda-terms and maps, we obtain various combinatorial specifications which allow us to access the distributions of pairs of related parameters such as: the number of bridges in rooted trivalent maps and of subterms in closed linear lambda-terms, the number of vertices of degree 1 in (1,3)-valent maps and of free variables in open linear lambda-terms etc. To analyse asymptotically these distributions, we introduce appropriate tools: a moment-pumping schema for differential equations and a composition schema inspired by Bender's theorem.
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