Large deviations of combinatorial distributions II: Local limit theorems
نویسنده
چکیده
This paper is a sequel to our paper [17] where we derived a general central limit theorem for probabilities of large deviations1 applicable to many classes of combinatorial structures and arithmetic functions; we consider corresponding local limit theorems in this paper. More precisely, given a sequence of integral random variables {Ωn}n≥1 each of maximal span 1 (see below for definition), we are interested in the asymptotic behavior of the probabilities
منابع مشابه
Large Deviations of Combinatorial Distributions I: Central Limit Theorems
We prove a general central limit theorem for probabilities of large deviations for sequences of random variables satisfying certain natural analytic conditions. This theorem has wide applications to combinatorial structures and to the distribution of additive arithmetical functions. The method of proof is an extension of Kubilius’ version of Cramér’s classical method based on analytic moment ge...
متن کاملLimit Theorems for the Number of Summands in Integer Partitions
Central and local limit theorems are derived for the number of distinct summands in integer partitions, with or without repetitions, under a general scheme essentially due to Meinardus. The local limit theorems are of the form of Cramér-type large deviations and are proved by Mellin transform and the two-dimensional saddle-point method. Applications of these results include partitions into posi...
متن کاملEquivalence of ensembles for two-species zero-range invariant measures
We study the equivalence of ensembles for stationary measures of interacting particle systems with two conserved quantities and unbounded local state space. The main motivation is a condensation transition in the zero-range process which has recently attracted attention. Establishing the equivalence of ensembles via convergence in specific relative entropy, we derive the phase diagram for the c...
متن کاملLarge Deviations Central Limit Theorems and L Convergence for Young Measures and Stochastic Homogenizations Julien Michel and Didier Piau
We study the stochastic homogenization processes consid ered by Baldi and by Facchinetti and Russo We precise the speed of convergence towards the homogenized state by proving the following results i a large deviations principle holds for the Young measures if the Young measures are evaluated on a given function then ii the speed of convergence is bounded in every L norm by an explicit rate and...
متن کاملLarge deviations for random walks under subexponentiality: the big-jump domain
For a given one-dimensional random walk {Sn} with a subexponential step-size distribution, we present a unifying theory to study the sequences {xn} for which P{Sn > x} ∼ nP{S1 > x} as n → ∞ uniformly for x ≥ xn. We also investigate the stronger ‘local’ analogue, P{Sn ∈ (x, x+T ]} ∼ nP{S1 ∈ (x, x + T ]}. Our theory is self-contained and fits well within classical results on domains of (partial) ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1997