Data structures with dynamical random transitions
We present a (non-standard) probabilistic analysis of dynamic data structures whose sizes are considered dynamic random walks. The basic operations (insertion, deletion, positive and negative queries, batched insertion, lazy deletion, etc.) are time-dependent random variables. This model is a (small) step toward the analysis of these structures when the distribution of the set of histories is not uniform. As an illustration, we focus on list structures (linear lists, priority queues, and dictionaries) but the technique is applicable as well to more advanced data structures.