law of large numbers渐近区域中的极限向前移动搜索代价
The limiting move-to-front search-cost in law of large numbers asymptotic regimes
摘要：
我们明确计算有限的瞬态分布的搜索成本的移动到前面的马尔可夫链时，对象的数量趋于无穷大，一般家庭的确定性或随机请求率。我们的技术是基于“随机分区的大数定律”，这是一个缩放限制，允许我们精确计算对象请求概率的经验泛函的极限期望。特别是，我们表明，有限的搜索成本可以在一个明确的确定性阈值分裂成一个随机变量的平衡，和第二个有关的列表的初始排序。我们的研究结果确保稳定的限制搜索成本下的一般扰动的请求概率。我们提供的限制瞬时性态的描述在几个例子中，只有固定制度是已知的，并讨论我们的标度限制的有效性范围。
英文摘要：
We explicitly compute the limiting transient distribution of the search-cost in the move-to-front Markov chain when the number of objects tends to infinity, for general families of deterministic or random request rates. Our techniques are based on a "law of large numbers for random partitions," a scaling limit that allows us to exactly compute limiting expectation of empirical functionals of the request probabilities of objects. In particular, we show that the limiting search-cost can be split at an explicit deterministic threshold into one random variable in equilibrium, and a second one related to the initial ordering of the list. Our results ensure the stability of the limiting search-cost under general perturbations of the request probabilities. We provide the description of the limiting transient behavior in several examples where only the stationary regime is known, and discuss the range of validity of our scaling limit.
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