概率年鉴发表现代概率论的研究论文，它与其他数学领域的关系，以及它在物理和生物科学中的应用。重点是重要性、兴趣和独创性——形式上的新颖性和正确性不足以发表。 《年鉴》还将发表权威的评论论文和对蓬勃发展领域的调查。

The Annals of Probability publishes research papers on modern probability theory, exploring its connections with other areas of mathematics and its applications in physical and biological sciences. The journal emphasizes the importance, interest, and originality of the papers; mere novelty and correctness are insufficient for publication. Additionally, the Annals will publish authoritative review papers and surveys of thriving fields.

《Annals of Probability》发表现代概率论的研究论文，探讨其与其他数学领域的关系，以及在物理和生物科学中的应用。期刊重点关注论文的重要性、趣味性和独创性，单纯的形式新颖性和正确性不足以满足发表要求。此外，《Annals of Probability》还会刊登权威的评论论文和对快速发展的领域的综述。

Annals of Probability

For polynomials in independent Wigner matrices, we prove convergence of the largest singular value to the operator norm of the corresponding polynomial in free semicircular variables, under fourth moment hypotheses. We actually prove a more general result of the form "no eigenvalues outside the support of the limiting eigenvalue distribution." We build on ideas of Haagerup–Schultz–Thorbjørnsen on the one hand and Bai–Silverstein on the other. We refine the linearization trick so as to preserve self-adjointness and we develop a secondary trick bearing on the calculation of correction terms. Instead of Poincaré-type inequalities, we use a variety of matrix identities and $L^{p}$ estimates. The Schwinger–Dyson equation controls much of the analysis.

Greg W. Anderson

The Annals of Probability

Convergence of the largest singular value of a polynomial in independent Wigner matrices

独立Wigner矩阵多项式最大奇异值的收敛性

For each s : 1,2... let n: r?(s) be a posit ive integer such that n/s --+ y > 0 as s --+ cc. Let V" be an n X s matrix whose entries are i.i.d. N(0, 1) random variables and let M": (I/s)V"V:.The random matrix V,V: is commonly referred to as the Wishart matrix W(1,, s). It is well known [Mar0enko and Pastur (1967), Wachter (1978)] that the empirical distribution function 4 of the eigenvalues of M, t.F"(r) = (I/n) x (number of eigenvalues of M " < *)l converges almost r.rr"ly ur r -+ oo to a nonrandom probability distribution function { having a density with positive support on [(1 tF)',(l + ,F>t], and when yi r, { yields additional mass on {0}. It is also known fGeman (1980)] that the maximum eigenvalue I(** of M" converges a.s. to (1 + ,F)'as s -+ oo. [The statement of thi. r"rult in Geman (1980) has all the M, constructed from one doubly infinite array of i.i.d. random variables. However, it is obvious from the proof that no relation on the entries of V" for different s is needed.] These results are established under assumptions more general on the entries of % than Gaussian distributed, involving conditions on the moments of these random variables. The present paper will prove the following

Jack W. Silverstein

Ann. Probab.

The Smallest Eigenvalue of a Large Dimensional Wishart Matrix

大维Wishart矩阵的最小特征值

Let $ X_1, X_2,\ldots$ be a sequence of free identically distributed random variables, with common distribution $\mu$. It was shown by Lindsay and Pata, in a more general context, that a sufficient condition for the weak law of large numbers to hold for the sequence $X_1, X_2,\ldots$ is that $$\lim_{t\to \infty}t\mu(\{x: |x|>t\}) = 0>$$ We show that this condition is necessary as well as sufficient. Even though the condition is identical with the corresponding one for commuting independent variables, the proof of the result uses the analytical techniques of free convolution theory, and it is quite different from the proof of the commutative theorem due to Kolmogorov.

Hari Bercovici

Vittorino Pata

The law of large numbers for free identically distributed random variables

自由同分布随机变量的大数定律

We prove the strong law of large numbers for a continuous-

M. Cranston

T. S. Mountford

The strong law of large numbers for a Brownian polymer

布朗聚合物的大数定律

Moderate deviation principles for stochastic differential equations driven by a Poisson random measure (PRM) in finite and infinite dimensions are obtained. Proofs are based on a variational representation for expected values of positive functionals of a PRM.

Amarjit Budhiraja

Paul Dupuis

Arnab Ganguly

Moderate deviation principles for stochastic differential equations with jumps

跳跃随机微分方程的中偏差原理

Diederik van Engelenburg

Tom Hutchcroft

The number of ends in the uniform spanning tree for recurrent unimodular random graphs

重现单模随机图上均匀生成树的端点数

Ahmed Bou-Rabee

Ewain Gwynne

Internal DLA on mated-CRT maps

配对CRT图上的内部DLA

Louigi Addario-Berry

Serte Donderwinkel

Random trees have height O(n)

随机树的高度为 O(n)

We consider percolation on the Voronoi tessellation generated by a homogeneous Poisson point process on the hyperbolic plane. We show that the critical probability for the existence of an infinite cluster is asymptotically equal to $\pi \lambda/3$ as $\lambda\to0.$ This answers a question of Benjamini and Schramm.

Abbreviation	Ann. Probab.
Journal Impact	2.19
Quartiles(Global)	STATISTICS & PROBABILITY(Q1)

ISSN	0091-1798, 2168-894X
h-index	99
Top Journals	Yes

Publication Information	Publisher: Institute of Mathematical Statistics，Publishing cycle: Bimonthly，Journal Type: journal，Open Access Journals: No
Basic data	Year of publication: 1996，Proportion of original research papers: 100.00%，Self Citation Rate:4.80%， Gold OA Rate: 0.52%
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 Probability

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