ABSTRACT For the critical branching random walk on the lattice , in the case of an arbitrary total number of produced offspring spreading on the lattice from the parental particle, the existence of a limit distribution (which corresponds to a steady state (or statistical equilibrium)) of the population is proved. If the second factorial moment of the total number of offspring is much larger than the square of the first factorial moment, then the limit particle field displays strong deviations from the uniformity: this is intermittency.

中文翻译：

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具有任意后代总数的临界分支随机游走中的稳态和间歇性

摘要 对于晶格上的临界分支随机游走，在从母粒子传播到晶格上的任意总数产生的后代的情况下，存在极限分布（对应于稳态（或统计平衡））的人口被证明。如果后代总数的二阶阶乘矩远大于第一阶阶矩的平方，则极限粒子场显示出与均匀性的强烈偏差：这就是间歇性。