Probability Theory and Related Fields

最新文章

• The likelihood ratio test in high-dimensional logistic regression is asymptotically a rescaled Chi-square AI翻译
  作者：Sur, Pragya; Chen, Yuxin; Candes, Emmanuel J.
  作者单位：Stanford University; Princeton University; Stanford University
  摘要：Logistic regression is used thousands of times a day to fit data, predict future outcomes, and assess the statistical significance of explanatory variables. When used for the purpose of statistical inference, logistic models produce p-values for the regression coefficients by using an approximation to the distribution of the likelihood-ratio test (LRT). Indeed, Wilks' theorem asserts that whenever we have a fixed number p of variables, twice the log-likelihood ratio (LLR) 2 Lambda is distribut...
• Scaling limit for the ant in a simple high-dimensional labyrinth AI翻译
  作者：Ben Arous, Gerard; Cabezas, Manuel; Fribergh, Alexander
  作者单位：New York University; Pontificia Universidad Catolica de Chile; Universite de Montreal
  摘要：We prove that, after suitable rescaling, the simple random walk on the trace of a large critical branching random walk in Zd converges to the Brownian motion on the integrated super-Brownian excursion when d>14.
• Weak universality for a class of 3d stochastic reaction-diffusion models AI翻译
  作者：Furlan, M.; Gubinelli, M.
  作者单位：Universite PSL; Universite Paris-Dauphine; University of Bonn; University of Bonn
  摘要：We establish the large scale convergence of a class of stochastic weakly nonlinear reaction-diffusion models on a three dimensional periodic domain to the dynamic phi 34 model within the framework of paracontrolled distributions. Our work extends previous results of Hairer and Xu to nonlinearities with a finite amount of smoothness (in particular C9 is enough). We use the Malliavin calculus to perform a partial chaos expansion of the stochastic terms and control their Lp norms in terms of the ...
• Edge statistics for a class of repulsive particle systems AI翻译
  作者：Kriecherbauer, Thomas; Venker, Martin
  作者单位：University of Bayreuth; Universite Catholique Louvain
  摘要：We study a class of interacting particle systems on R which was recently investigated by Gotze and Venker (Ann Probab 42(6): 2207-2242, 2014. doi: 10.1214/ 13-AOP844). These ensembles generalize eigenvalue ensembles of Hermitian random matrices by allowing different interactions between particles. Although these ensembles are not known to be determinantal one can use the stochastic linearization method of Gotze and Venker (Ann Probab 42(6): 2207-2242, 2014. doi: 10.1214/13-AOP844) to represent...
• Limit theorems in bi-free probability theory AI翻译
  作者：Hasebe, Takahiro; Huang, Hao-Wei; Wang, Jiun-Chau
  作者单位：Hokkaido University; National Sun Yat Sen University; University of Saskatchewan
  摘要：In this paper additive bi-free convolution is defined for general Borel probability measures, and the limiting distributions for sums of bi-free pairs of self-adjoint commuting random variables in an infinitesimal triangular array are determined. These distributions are characterized by their bi-freely infinite divisibility, and moreover, a transfer principle is established for limit theorems in classical probability theory and Voiculescu's bi-free probability theory. Complete descriptions of ...
• On the energy landscape of the mixed even p-spin model AI翻译
  作者：Chen, Wei-Kuo; Handschy, Madeline; Lerman, Gilad
  作者单位：University of Minnesota System; University of Minnesota Twin Cities
  摘要：We investigate the energy landscape of the mixed even p-spin model with Ising spin configurations. We show that for any given energy level between zero and the maximal energy, with overwhelming probability there exist exponentially many distinct spin configurations such that their energies stay near this energy level. Furthermore, their magnetizations and overlaps are concentrated around some fixed constants. In particular, at the level of maximal energy, we prove that the Hamiltonian exhibits...
• Sharpness of the phase transition for continuum percolation in R2 AI翻译
  作者：Ahlberg, Daniel; Tassion, Vincent; Teixeira, Augusto
  作者单位：Uppsala University; University of Geneva
  摘要：We study the phase transition of random radii Poisson Boolean percolation: Around each point of a planar Poisson point process, we draw a disc of random radius, independently for each point. The behavior of this process is well understood when the radii are uniformly bounded from above. In this article, we investigate this process for unbounded (and possibly heavy tailed) radii distributions. Under mild assumptions on the radius distribution, we show that both the vacant and occupied sets unde...
• Orderings of weakly correlated random variables, and prime number races with many contestants AI翻译
  作者：Harper, Adam J.; Lamzouri, Youness
  作者单位：University of Cambridge; University of Warwick; York University - Canada
  摘要：We investigate the race between prime numbers in many residue classes modulo q, assuming the standard conjectures GRH and LI. Among our results we exhibit, for the first time, n-way prime number races modulo q where the biases do not dissolve when n, q -> infinity. We also study the leaders in the prime number race, obtaining asymptotic formulae for logarithmic densities when the number of competitors can be as large as a power of q, whereas previous methods could only allow a power of log q. ...
• Equivalence of Palm measures for determinantal point processes governed by Bergman kernels AI翻译
  作者：Bufetov, Alexander I.; Fan, Shilei; Qiu, Yanqi
  作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Aix-Marseille Universite; Russian Academy of Sciences; Steklov Mathematical Institute of the Russian Academy of Sciences; Kharkevich Institute for Information Transmission Problems of the RAS; HSE University (National Research University Higher School of Economics); Saint Petersburg State University; Central China Normal University; Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Centre National de la Recherche Scientifique (CNRS); Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS
  摘要：For a determinantal point process induced by the reproducing kernel of the weighted Bergman space A2(U,.) over a domain U. Cd, we establish the mutual absolute continuity of reduced Palm measures of any order provided that the domain U contains a non-constant bounded holomorphic function. The result holds in all dimensions. The argument uses the H 8 (U)-module structure of A2(U,.). A corollary is the quasi-invariance of our determinantal point process under the natural action of the group of c...
• Couplings, gradient estimates and logarithmic Sobolev inequalitiy for Langevin bridges AI翻译
  作者：Conforti, Giovanni; Von Renesse, Max
  作者单位：Institut Polytechnique de Paris; Ecole Polytechnique; ENSTA Paris; Leipzig University
  摘要：In this paper we establish quantitative results about the bridges of the Langevin dynamics and the associated reciprocal processes. They include an equivalence between gradient estimates for bridge semigroups and couplings, comparison principles, bounds of the distance between bridges of different Langevin dynamics, and a logarithmic Sobolev inequality for bridge measures. The existence of an invariant measure for the bridges is also discussed and quantitative bounds for the convergence to the...