Asymptotic formula for a partition function of reversible coagulation-fragmentation processes

Gregory A. Freiman; Boris L. Granovsky

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Asymptotic formula for a partition function of reversible coagulation-fragmentation processes

机译：可逆凝结-破碎过程分配函数的渐近公式

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摘要

We construct a probability model seemingly unrelated to the considered stochastic process of coagulation and fragmentation. By proving for this model the local limit theorem, we establish the asymptotic formula for the partition function of the equilibrium measure for a wide class of parameter functions of the process. This formula proves the conjecture stated in [5] for the above class of processes. The method used goes back to A. Khintchine.

机译：我们构建了一个似乎与所考虑的随机凝结和破碎过程无关的概率模型。通过证明该模型的局部极限定理，我们为过程的各种参数函数建立了平衡测度分配函数的渐近公式。该公式证明了上述过程类别在[5]中所述的猜想。使用的方法可以追溯到A. Khintchine。

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《Israel Journal of Mathematics》 |2002年第1期|259-279|共21页
作者
Gregory A. Freiman; Boris L. Granovsky;
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School of Mathematical Sciences Raymond and Beverly Sackler Faculty of Exact Sciences Tel Aviv University;

Department of Mathematics Technion-Israel Institute of Technology;

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1. Reversible coagulation-fragmentation processes and random combinatorial structures: Asymptotics for the number of groups [J] . Erlihson MM, Granovsky BL Random structures & algorithms . 2004,第2期

机译：可逆的凝结-破碎过程和随机组合结构：组数的渐近性
2. Asymptotics of Certain Coagulation-Fragmentation Processes and Invariant Poisson-Dirichlet Measures [J] . Mayer-Wolf Eddy, Zeitouni Ofer, Zerner Martin P.W. Electronic Journal of Probability . 2002,第5a8期

机译：某些凝块破碎过程的渐近性和不变泊松-狄利克雷特测度
3. The asymptotic behavior in a reversible random coagulation-fragmentation polymerization process with sub-exponential decay [J] . Siqun Dong, Dianli Zhao Physica, A. Statistical mechanics and its applications . 2018,第期

机译：具有亚指数衰减的可逆随机凝血 - 碎片聚合过程中的渐近行为
4. The Asymptotic Behavior of Heterogeneous Coagulation-Fragmentation Processes [C] . Chunhua Hu International Congress on Complexity System and Engineering Management . 2013

机译：异质凝血 - 破碎过程的渐近行为
5. Growth processes on formulas and reversible circuits [D] . Brodsky, Alexander 2003

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6. Rate Distortion Function of Gaussian Asymptotically WSS Vector Processes [O] . Jesús Gutiérrez-Gutiérrez, Marta Zárraga-Rodríguez, Pedro M. Crespo, 2018

机译：高斯渐近WSS矢量进程的速率失真函数
7. Asymptotic formula for a partition function of reversible coagulation -fragmentation processes [O] . Freiman, Gregory, Granovsky, Boris 2002

机译：可逆凝固分配函数的渐近公式 - 碎片整理过程
8. An Asymptotic Formula for the Prolate Spheroidal Radial Function of the Third Kind. [R] . lauchle, g. c. 1976

机译：第三类扁长球形径向函数的渐近公式。

Asymptotic formula for a partition function of reversible coagulation-fragmentation processes

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