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Random trees and applications
random tree contour process conditioned tree Brownian motion Brownian excursion real tree coding of trees
2009/5/18
We discuss several connections between discrete and continuous random trees. In the discrete setting, we focus on Galton-Watson trees under various conditionings. In particular, we present a simple ap...
Large deviations and stochastic calculus for large random matrices
large deviations random matrices non-commutative measure integration.
2009/5/18
Large random matrices appear in different fields of mathematics and physics such as combinatorics, probability theory, statistics, operator theory, number theory, quantum field theory, string theory e...
Uniqueness and non-uniqueness in percolation theory
percolation uniqueness of the infinite cluster transitive graphs amenability
2009/5/18
This paper is an up-to-date introduction to the problem of uniqueness versus non-uniqueness of infinite clusters for percolation on $Z^d$ and more generally on transitive graphs. For iid percolation o...
Localization and delocalization of random interfaces
random interfaces random surfaces roughening entropic repulsion pinning wetting prewetting
2009/5/18
The study of effective interface models has been quite active recently, with a particular emphasis on the effect of various external potentials (wall, pinning potential, ...) leading to localization/d...
Motivated by Segal's axiom of conformal field theory, we do a survey on geometrical random fields. We do a history in order to arrive at a field theoretical analog of Klauder's quantization in Hamilto...
Martingale proofs of many-server heavy-traffic limits for Markovian queues
multiple-server queues many-server heavy-traffic limits for queues diffusion approximations martingales functional central limit theorems
2009/5/18
This is an expository review paper illustrating the “martin- gale method” for proving many-server heavy-traffic stochastic-process limits for queueing models, supporting diffusion-process approximatio...
Queueing networks constitute a large family of stochastic models, involving jobs that enter a network, compete for service, and eventually leave the network upon completion of service. Since the early...
Loop-Erased Walks Intersect Infinitely Often in Four Dimensions
Random Walks Loop-Erased Walks Intersections
2009/5/8
In this short note we show that the paths two independent loop-erased random walks in four dimensions intersect infinitely often. We actually prove the stronger result that the cut-points of the two w...
Brownian couplings, convexity, and shy-ness
Brownian motion co-adapted coupling convexity coupling Markovian coupling perversecoupling reflection coupling
2009/4/29
Benjamini, Burdzy and Chen (2007) introduced the notion of a shy coupling: a coupling of a Markov process such that, for suitable starting points, there is a positive chance of the two component proce...
Oscillation and Non-oscillation in Solutions of Nonlinear Stochastic Delay Differential Equations
Stochastic delay dierential equation oscillation non-Coscillatio
2009/4/28
This paper studies the oscillation and nonoscillation of solutions of a nonlinear stochastic delay differential equation, where the noise perturbation depends on the current state, and the drift depen...
Poisson Statistics for the Largest Eigenvalues of Wigner Random Matrices with Heavy Tails
random matrices largest eigenvalues Poisson statistics
2009/4/28
We study large Wigner random matrices in the case when the marginal distributions of matrix entries have heavy tails. We prove that the largest eigenvalues of such matrices have Poisson statistics.
山西省晋中地区外商投资企业调查报告
山西省 晋中地区 外商投资企业 调查报告
2009/4/14
山西省晋中地区外商投资企业的调查于1997年8月26日在全地区进行。根据晋中地区国税局所掌握的资料,对其有一定代表性的43家企业进行调查。得到了能反映本地区外商投资企业运营状况的具体资料。调查结果表明:改革开放以来,晋中地区外商投资企业不断扩大,特别是在93、94两年之间迅速增加,对我国的对外开放发挥了巨大的作用;根据山西的特点以及晋中地区的优势看,该地区外商投资在选煤,炼焦方面的几家企业规模较大...
一名统计学家遇到一位数学家,统计学家调侃数学家说道:“你们不是说若x=y且y=z,则x=z吗!那么想必你若是喜欢一个女孩,那么那个女孩喜欢的男孩你也会喜欢喽!?”数学家想了一下反问道:“那么你把左手放到一锅一百度的开水中,右手放到一锅零度的冰水里想来也没事吧!因为它们平均的温度不过是五十度而已!”