Limit shapes of multiplicative measures associated with coagulation-fragmentation processes and rand
Limit shapes of multiplicative measures associated with coagulation-fragmentation processes and rand
复制标题
与凝固破碎过程和兰特相关的乘法测量的极限形状
DOI：
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发表时间：
2005
期刊：
影响因子：
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通讯作者：
B. Granovsky
中科院分区：
文献类型：
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作者：
Michael M. Erlihson;B. Granovsky
我们找到了由带扩张参数的指数生成函数$a_ksim Ck^{p-1}，k诱导的一类乘法测度族在划分集上的极限形状 oinfty，p> 0 $，其中$C$为正常数。考虑的措施与可逆的凝聚-碎裂过程和某些组合结构，称为组件。从尺度随机分拆的极限形状出发，证明了其涨落的泛函中心极限定理。我们证明，当组件的大小超过阈值时，组件的数量的独立性转化为它们的条件独立性。除其他事项外，本文还讨论了，在一般情况下，极限形状，阈值和凝胶化之间的相互作用。
We find limit shapes for a family of multiplicative measures on the set of partitions, induced by exponential generating functions with expansive parameters, $a_ksim Ck^{p-1}, k oinfty, p>0$,where $C$ is a positive constant. The measures considered are associated with reversible coagulation-fragmentation processes and certain combinatorial structures, known as assemblies. We prove the functional central limit theorem for the fluctuations of a scaled random partition from its limit shape. We demonstrate that when the component size passes beyond the threshold value, the independence of numbers of components transforms into their conditional independence. Among other things, the paper also discusses, in a general setting, the interplay between limit shapes, threshold and gelation.