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作者：Croydon, David A.
作者单位：University of Warwick
摘要：In this article, a localisation result is proved for the biased random walk on the range of a simple random walk in high dimensions (). This demonstrates that, unlike in the supercritical percolation setting, a slowdown effect occurs as soon as a non-trivial bias is introduced. The proof applies a decomposition of the underlying simple random walk path at its cut-times to relate the associated biased random walk to a one-dimensional random walk in a random environment in Sinai's regime. Via th...
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作者：Kargin, V.
作者单位：University of Cambridge
摘要：It is shown that the normalized fluctuations of Riemann's zeta zeros around their predicted locations follow the Gaussian law. It is also shown that fluctuations of two zeros,gamma k and gamma k+x, with x similar to (log k)(beta), beta > 0, for large k follow the two-variate Gaussian distribution with correlation (1 - beta)(+).
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作者：Bauerschmidt, Roland
作者单位：University of British Columbia
摘要：We present a simple method to decompose the Green forms corresponding to a large class of interesting symmetric Dirichlet forms into integrals over symmetric positive semi-definite and finite range (properly supported) forms that are smoother than the original Green form. This result gives rise to multiscale decompositions of the associated Gaussian free fields into sums of independent smoother Gaussian fields with spatially localized correlations. Our method makes use of the finite propagatio...
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作者：Belius, David
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：This work proves that the fluctuations of the cover time of simple random walk in the discrete torus of dimension at least three with large side-length are governed by the Gumbel extreme value distribution. This result was conjectured for example in Aldous and Fill (Reversible Markov chains and random walks on graphs, in preparation). We also derive some corollaries which qualitatively describe how covering happens. In addition, we develop a new and stronger coupling of the model of random int...
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作者：Bloemendal, Alex; Virag, Balint
作者单位：Harvard University; University of Toronto; University of Toronto
摘要：Given a large, high-dimensional sample from a spiked population, the top sample covariance eigenvalue is known to exhibit a phase transition. We show that the largest eigenvalues have asymptotic distributions near the phase transition in the rank one spiked real Wishart setting and its general beta analogue, proving a conjecture of Baik et al. (Ann Probab 33:1643-1697, 2005). We also treat shifted mean Gaussian orthogonal and beta ensembles. Such results are entirely new in the real case; in t...
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作者：Yattselev, Maxim L.
作者单位：University of Oregon
摘要：A two-dimensional statistical model of N charged particles interacting via logarithmic repulsion in the presence of an oppositely charged regular closed region K whose charge density is determined by its equilibrium potential at an inverse temperature beta is investigated. When the charge on the region, s, is greater than N, the particles accumulate in a neighborhood of the boundary of K, and form a point process in the complex plane. We describe the weak* limits of the joint intensities of th...
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作者：Hammond, Alan; Sheffield, Scott
作者单位：University of Oxford; Massachusetts Institute of Technology (MIT)
摘要：We introduce a natural family of random walks S-n on Z that scale to fractional Brownian motion. The increments X-n := S-n - Sn-1 is an element of {+/- 1} have the property that given {X-k : k < n}, the conditional law of X-n is that of Xn-kn, where k(n) is sampled independently from a fixed law mu on the positive integers. When mu has a roughly power law decay (precisely, when mu lies in the domain of attraction of an alpha-stable subordinator, for 0 < alpha < 1/2) the walks scale to fraction...
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作者：del Barrio, Eustasio; Matran, Carlos
作者单位：Universidad de Valladolid
摘要：We consider a class of partial mass problems in which a fraction of the mass of a probability measure is allowed to be changed (trimmed) to maximize fit to a given pattern. This includes the problem of optimal partial transportation of mass, where a part of the mass need not be transported, and also trimming procedures which are often used in statistical data analysis to discard outliers in a sample (the data with lowest agreement to a certain pattern). This results in a modified, trimmed vers...
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作者：Quastel, Jeremy; Remenik, Daniel
作者单位：University of Toronto; Universidad de Chile
摘要：We obtain a formula for the -dimensional distributions of the process in terms of a Fredholm determinant on , as opposed to the standard formula which involves extended kernels, on . The formula is analogous to an earlier formula of Prahofer and Spohn (J Stat Phys 108(5-6):1071-1106, 2002) for the process. Using this formula we are able to prove that the process is Holder continuous with exponent -and that it fluctuates locally like a Brownian motion. We also explain how the same methods can b...
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作者：van Handel, Ramon
作者单位：Princeton University
摘要：Let F be a separable uniformly bounded family of measurable functions on a standard measurable space (X, X, and let N-[](F, epsilon, mu) be the smallest number of epsilon-brackets in L-1(mu) needed to cover F. The following are equivalent: F is a universal Glivenko-Cantelli class. N-[](F, epsilon, mu) < infinity for every epsilon > 0 and every probability measure mu. F is totally bounded in L-1(mu) for every probability measure mu. F does not contain a Boolean sigma-independent sequence. It fo...
