405,320 research outputs found

    Recurrence of cocycles and stationary random walks

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    We survey distributional properties of Rd\mathbb{R}^d-valued cocycles of finite measure preserving ergodic transformations (or, equivalently, of stationary random walks in Rd\mathbb{R}^d) which determine recurrence or transience.Comment: Published at http://dx.doi.org/10.1214/074921706000000112 in the IMS Lecture Notes--Monograph Series (http://www.imstat.org/publications/lecnotes.htm) by the Institute of Mathematical Statistics (http://www.imstat.org

    New exact solutions for power-law inflation Friedmann models

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    We consider the spatially flat Friedmann model. For a(t) = t^p, especially, if p is larger or equal to 1, this is called power-law inflation. For the Lagrangian L = R^m with p = - (m - 1)(2m - 1)/(m - 2), power-law inflation is an exact solution, as it is for Einstein gravity with a minimally coupled scalar field Phi in an exponential potential V(Phi) = exp(mu Phi) and also for the higher-dimensional Einstein equation with a special Kaluza-Klein ansatz. The synchronized coordinates are not adapted to allow a closed-form solution, so we use another gauge. Finally, special solutions for the closed and open Friedmann model are found.Comment: 9 pages, LaTeX, reprinted from Astron. Nachr. 311 (1990) 16

    The Parabolic Anderson Model with Acceleration and Deceleration

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    We describe the large-time moment asymptotics for the parabolic Anderson model where the speed of the diffusion is coupled with time, inducing an acceleration or deceleration. We find a lower critical scale, below which the mass flow gets stuck. On this scale, a new interesting variational problem arises in the description of the asymptotics. Furthermore, we find an upper critical scale above which the potential enters the asymptotics only via some average, but not via its extreme values. We make out altogether five phases, three of which can be described by results that are qualitatively similar to those from the constant-speed parabolic Anderson model in earlier work by various authors. Our proofs consist of adaptations and refinements of their methods, as well as a variational convergence method borrowed from finite elements theory.Comment: 19 page

    Central limit theorems for Poisson hyperplane tessellations

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    We derive a central limit theorem for the number of vertices of convex polytopes induced by stationary Poisson hyperplane processes in Rd\mathbb{R}^d. This result generalizes an earlier one proved by Paroux [Adv. in Appl. Probab. 30 (1998) 640--656] for intersection points of motion-invariant Poisson line processes in R2\mathbb{R}^2. Our proof is based on Hoeffding's decomposition of UU-statistics which seems to be more efficient and adequate to tackle the higher-dimensional case than the ``method of moments'' used in [Adv. in Appl. Probab. 30 (1998) 640--656] to treat the case d=2d=2. Moreover, we extend our central limit theorem in several directions. First we consider kk-flat processes induced by Poisson hyperplane processes in Rd\mathbb{R}^d for 0kd10\le k\le d-1. Second we derive (asymptotic) confidence intervals for the intensities of these kk-flat processes and, third, we prove multivariate central limit theorems for the dd-dimensional joint vectors of numbers of kk-flats and their kk-volumes, respectively, in an increasing spherical region.Comment: Published at http://dx.doi.org/10.1214/105051606000000033 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

    Limit theorems for functionals on the facets of stationary random tessellations

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    We observe stationary random tessellations X={Ξn}n1X=\{\Xi_n\}_{n\ge1} in Rd\mathbb{R}^d through a convex sampling window WW that expands unboundedly and we determine the total (k1)(k-1)-volume of those (k1)(k-1)-dimensional manifold processes which are induced on the kk-facets of XX (1kd11\le k\le d-1) by their intersections with the (d1)(d-1)-facets of independent and identically distributed motion-invariant tessellations XnX_n generated within each cell Ξn\Xi_n of XX. The cases of XX being either a Poisson hyperplane tessellation or a random tessellation with weak dependences are treated separately. In both cases, however, we obtain that all of the total volumes measured in WW are approximately normally distributed when WW is sufficiently large. Structural formulae for mean values and asymptotic variances are derived and explicit numerical values are given for planar Poisson--Voronoi tessellations (PVTs) and Poisson line tessellations (PLTs).Comment: Published at http://dx.doi.org/10.3150/07-BEJ6131 in the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

    Tame class field theory for arithmetic schemes

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    We extend the unramified class field theory for arithmetic schemes of K. Kato and S. Saito to the tame case. Let XX be a regular proper arithmetic scheme and let DD be a divisor on XX whose vertical irreducible components are normal schemes. Theorem: There exists a natural reciprocity isomorphism \rec_{X,D}: \CH_0(X,D) \liso \tilde \pi_1^t(X,D)^\ab\. Both groups are finite. This paper corrects and generalizes my paper "Relative K-theory and class field theory for arithmetic surfaces" (math.NT/0204330
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