应用概率年鉴旨在发表反映当代应用概率各个方面的最高质量研究。主要强调重要性和独创性。

The Annals of Applied Probability aims to publish high-quality research that reflects various aspects of contemporary applied probability. The journal places a strong emphasis on the significance and originality of the research.

《Annals of Applied Probability》旨在发表高质量的研究成果，涵盖当代应用概率的各个方面。期刊特别强调研究的重要性和独创性。

Annals of Applied Probability

Consider an N×n random matrix Yn=(Ynij) where the entries are given by $Y^{n}_{ij}=\frac{\sigma_{ij}(n)}{\sqrt{n}}X^{n}_{ij}$, the Xnij being independent and identically distributed, centered with unit variance and satisfying some mild moment assumption. Consider now a deterministic N×n matrix An whose columns and rows are uniformly bounded in the Euclidean norm. Let Σn=Yn+An. We prove in this article that there exists a deterministic N×N matrix-valued function Tn(z) analytic in ℂ−ℝ+ such that, almost surely, $$\lim_{n\rightarrow+\infty,N/n\rightarrow c}\biggl(\frac{1}{N}\operatorname{Trace}(\Sigma_{n}\Sigma_{n}^{T}-zI_{N})^{-1}-\frac{1}{N}\operatorname{Trace}T_{n}(z)\biggr )=0.$$ Otherwise stated, there exists a deterministic equivalent to the empirical Stieltjes transform of the distribution of the eigenvalues of ΣnΣnT. For each n, the entries of matrix Tn(z) are defined as the unique solutions of a certain system of nonlinear functional equations. It is also proved that $\frac{1}{N}\operatorname{Trace}\ T_{n}(z)$ is the Stieltjes transform of a probability measure πn(dλ), and that for every bounded continuous function f, the following convergence holds almost surely $$\frac{1}{N}\sum_{k=1}^{N}f(\lambda_{k})-\int_{0}^{\infty}f(\lambda)\pi _{n}(d\lambda)\mathop{\longrightarrow}_{n\rightarrow\infty}0,$$ where the (λk)1≤k≤N are the eigenvalues of ΣnΣnT. This work is motivated by the context of performance evaluation of multiple inputs/multiple output (MIMO) wireless digital communication channels. As an application, we derive a deterministic equivalent to the mutual information: $$C_{n}(\sigma^{2})=\frac{1}{N}\mathbb{E}\log \det\biggl(I_{N}+\frac{\Sigma_{n}\Sigma_{n}^{T}}{\sigma^{2}}\biggr),$$ where σ2 is a known parameter.

Walid Hachem

Philippe Loubaton

Jamal Najim

The Annals of Applied Probability

Deterministic equivalents for certain functionals of large random matrices

大型随机矩阵某些泛函的确定性等价

We study the asymptotic optimal control of multi-class restless bandits. A restless bandit is a controllable stochastic process whose state evolution depends on whether or not the bandit is made active. Since finding the optimal control is typically intractable, we propose a class of priority policies that are proved to be asymptotically optimal under a global attractor property and a technical condition. We consider both a fixed population of bandits as well as a dynamic population where bandits can depart and arrive. As an example of a dynamic population of bandits, we analyze a multi-class $\mathit{M/M/S+M}$ queue for which we show asymptotic optimality of an index policy. We combine fluid-scaling techniques with linear programming results to prove that when bandits are indexable, Whittle's index policy is included in our class of priority policies. We thereby generalize a result of Weber and Weiss [J. Appl. Probab. 27 (1990) 637–648] about asymptotic optimality of Whittle's index policy to settings with (i) several classes of bandits, (ii) arrivals of new bandits and (iii) multiple actions. Indexability of the bandits is not required for our results to hold. For nonindexable bandits, we describe how to select priority policies from the class of asymptotically optimal policies and present numerical evidence that, outside the asymptotic regime, the performance of our proposed priority policies is nearly optimal.

I. M. Verloop

Asymptotically optimal priority policies for indexable and nonindexable restless bandits

渐近最优优先策略用于可索引和不可索引的活跃强盗问题

Souvik Dhara

Debankur Mukherjee

Kavita Ramanan

On r-to-p norms of random matrices with nonnegative entries: Asymptotic normality and ℓ∞-bounds for the maximizer

关于非负元素随机矩阵的r-to-p范数：最大化子的渐近正态性和ℓ∞界

Xinxin Chen

Christophe Garban

Atul Shekhar

Domain of attraction of the fixed points of Branching Brownian motion

分支布朗运动固定点的吸引域

Alain Durmus

Andreas Eberle

Aurélien Enfroy

Arnaud Guillin

Pierre Monmarché

Discrete sticky couplings of functional autoregressive processes

功能自回归过程的离散粘性耦合

Yucheng Liu

Continuous-time weakly self-avoiding walk on Z has strictly monotone escape speed

Abbreviation	Ann. Appl. Probab.
Journal Impact	1.43
Quartiles(Global)	STATISTICS & PROBABILITY(Q2)

ISSN	1050-5164, 2168-8737
h-index	89

Publication Information	Publisher: Institute of Mathematical Statistics，Publishing cycle: Quarterly，Journal Type: journal，Open Access Journals: No
Basic data	Year of publication: 1996，Proportion of original research papers: 100.00%，Self Citation Rate:7.10%， Gold OA Rate: 1.64%
Average review cycle	网友分享经验：较慢,6-12周
Average recruitment ratio	网友分享经验：容易

Annals of Applied Probability

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Deterministic equivalents for certain functionals of large random matrices

Asymptotically optimal priority policies for indexable and nonindexable restless bandits

On r-to-p norms of random matrices with nonnegative entries: Asymptotic normality and ℓ∞-bounds for the maximizer

Domain of attraction of the fixed points of Branching Brownian motion

Discrete sticky couplings of functional autoregressive processes

On r-to-p norms of random matrices with nonnegative entries: Asymptotic normality and ℓ∞-bounds for the maximizer

Domain of attraction of the fixed points of Branching Brownian motion

Discrete sticky couplings of functional autoregressive processes

Continuous-time weakly self-avoiding walk on Z has strictly monotone escape speed

Gibbs equilibrium fluctuations of point vortex dynamics