Stochastic integral representation of the $L^{2}$ modulus of Brownian local time and a central limit theorem [PDF]
, 2009 The purpose of this note is to prove a central limit theorem for the $L^2$-modulus of continuity of the Brownian local time obtained in \cite{CLMR}, using techniques of stochastic analysis.
Hu, Yaozhong, Nualart, David
core +2 more sources
Local Limit Theorems for Sample Extremes
The Annals of Probability, 1981 Assuming von Mises type conditions, we can prove the density of the normalized maximum of i.i.d. random variables converges to the density of the appropriate extreme value distribution in the Lp metric, p≤∞ provided both F’ and the limit extreme value density are in the space Lp.
de Haan, L., Resnick, S. I.
openaire +3 more sources
Inverse Limit Shape Problem for Multiplicative Ensembles of Convex Lattice Polygonal Lines
Mathematics, 2023 Convex polygonal lines with vertices in Z+2 and endpoints at 0=(0,0) and n=(n1,n2)→∞, such that n2/n1→c∈(0,∞), under the scaling n1−1, have limit shape γ* with respect to the uniform distribution, identified as the parabola arc c(1−x1)+x2=c.
Leonid V. Bogachev +1 more
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The Euclid Algorithm is totally gaussian [PDF]
Discrete Mathematics & Theoretical Computer Science, 2012 We consider Euclid’s gcd algorithm for two integers $(p, q)$ with $1 \leq p \leq q \leq N$, with the uniform distribution on input pairs. We study the distribution of the total cost of execution of the algorithm for an additive cost function $d$ on the ...
Brigitte Vallée
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Isotropic random walks on affine buildings [PDF]
, 2005 In this paper we apply techniques of spherical harmonic analysis to prove a local limit theorem, a rate of escape theorem, and a central limit theorem for isotropic random walks on arbitrary thick regular affine buildings of irreducible type.Comment: To ...
Parkinson, James
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The distribution of m-ary search trees generated by van der Corput sequences [PDF]
Discrete Mathematics & Theoretical Computer Science, 2004 We study the structure of m-ary search trees generated by the van der Corput sequences. The height of the tree is calculated and a generating function approach shows that the distribution of the depths of the nodes is asymptotically normal ...
Wolfgang Steiner
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A local limit theorem for coefficients of modified Borwein's method
Glasnik Matematicki - Serija III, 2019 The paper extends the study of the modified Borwein method for the calculation of the Riemann zeta-function. It presents an alternative perspective on the proof of a local limit theorem for coefficients of the method.
I. Belovas
semanticscholar +1 more source
The Almost Sure Local Central Limit Theorem for the Negatively Associated Sequences
Journal of Applied Mathematics, 2013 In this paper, the almost sure central limit theorem is established for sequences of negatively associated random variables: limn→∞(1/logn)∑k=1n(I(ak ...
Yuanying Jiang, Qunying Wu
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On mixing and the local central limit theorem for hyperbolic flows [PDF]
Ergodic Theory and Dynamical Systems, 2017 We formulate abstract conditions under which a suspension flow satisfies the local central limit theorem. We check the validity of these conditions for several systems including reward renewal processes, Axiom A flows, as well as the systems admitting ...
D. Dolgopyat, P'eter N'andori
semanticscholar +1 more source
Local limit theorem and equivalence of dynamic and static points of view for certain ballistic random walks in i.i.d. environments [PDF]
, 2014 In this work, we discuss certain ballistic random walks in random environments on $\mathbb{Z}^d$, and prove the equivalence between the static and dynamic points of view in dimension $d\geq4$.
Noam Berger, Moran Cohen, Ron Rosenthal
semanticscholar +1 more source