Rates of Poisson convergence for some coverage and urn problems using coupling

1988 ◽  
Vol 25 (4) ◽  
pp. 717-724 ◽  
Author(s):  
L. Holst ◽  
J. E. Kennedy ◽  
M. P. Quine
Keyword(s):  
Rate Of Convergence ◽  
Coupling Inequality ◽  
Variation Distance ◽  
Occupancy Problems

Bounds on the rate of convergence measured by the variation distance are obtained for the number of large spacings and for two occupancy problems connected with multinomial and Pólya sampling. The bounds are derived by imbedding techniques together with the elementary coupling inequality.

Rates of Poisson convergence for some coverage and urn problems using coupling

1988 ◽  
Vol 25 (04) ◽  
pp. 717-724 ◽  
Author(s):  
L. Holst ◽  
J. E. Kennedy ◽  
M. P. Quine
Keyword(s):  
Rate Of Convergence ◽  
Coupling Inequality ◽  
Variation Distance ◽  
Occupancy Problems

Bounds on the rate of convergence measured by the variation distance are obtained for the number of large spacings and for two occupancy problems connected with multinomial and Pólya sampling. The bounds are derived by imbedding techniques together with the elementary coupling inequality.

Mixing rates for Brownian motion in a convex polyhedron

1990 ◽  
Vol 27 (2) ◽  
pp. 259-268 ◽  
Author(s):  
Peter Matthews
Keyword(s):  
Brownian Motion ◽  
Rate Of Convergence ◽  
Convex Polyhedron ◽  
Upper Bounds ◽  
Convergence In Distribution ◽  
Convex Polyhedral ◽  
Variation Distance ◽  
Mixing Rates

For Brownian motion on a convex polyhedral subset of a sphere or torus, the rate of convergence in distribution to uniformity is studied. The main result is a method to take a Markov coupling on the full sphere or torus and create a faster coupling on the convex polyhedral subset. Upper bounds on variation distance are computed, and applications are discussed.

Mixing rates for Brownian motion in a convex polyhedron

1990 ◽  
Vol 27 (02) ◽  
pp. 259-268
Author(s):  
Peter Matthews
Keyword(s):  
Brownian Motion ◽  
Rate Of Convergence ◽  
Convex Polyhedron ◽  
Upper Bounds ◽  
Convergence In Distribution ◽  
Convex Polyhedral ◽  
Variation Distance ◽  
Mixing Rates

For Brownian motion on a convex polyhedral subset of a sphere or torus, the rate of convergence in distribution to uniformity is studied. The main result is a method to take a Markov coupling on the full sphere or torus and create a faster coupling on the convex polyhedral subset. Upper bounds on variation distance are computed, and applications are discussed.

scholarly journals Rate of Convergence of the Short Cycle Distribution in Random Regular Graphs Generated by Pegging

10.37236/133 ◽  
2009 ◽  
Vol 16 (1) ◽  
Author(s):  
Pu Gao ◽  
Nicholas Wormald
Keyword(s):  
Rate Of Convergence ◽  
Total Variation ◽  
Upper Bound ◽  
Mixing Time ◽  
Limiting Distribution ◽  
Total Variation Distance ◽  
Regular Graphs ◽  
Short Cycle ◽  
Variation Distance

The pegging algorithm is a method of generating large random regular graphs beginning with small ones. The $\epsilon$-mixing time of the distribution of short cycle counts of these random regular graphs is the time at which the distribution reaches and maintains total variation distance at most $\epsilon$ from its limiting distribution. We show that this $\epsilon$-mixing time is not $o(\epsilon^{-1})$. This demonstrates that the upper bound $O(\epsilon^{-1})$ proved recently by the authors is essentially tight.

On the rate of convergence in the central limit theorem for hierarchical Laplacians

2019 ◽  
Vol 23 ◽  
pp. 68-81
Author(s):  
Alexander Bendikov ◽  
Wojciech Cygan
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Normal Distribution ◽  
Rate Of Convergence ◽  
Ultrametric Space ◽  
Standard Normal Distribution ◽  
Arithmetic Means ◽  
The Central Limit Theorem ◽  
Standard Normal ◽  
Variation Distance

Let (X,d) be a proper ultrametric space. Given a measuremonXand a functionB↦C(B) defined on the set of all non-singleton ballsBwe consider the hierarchical LaplacianL=LC. Choosing a sequence {ε(B)} of i.i.d. random variables we define the perturbed functionC(B,ω) and the perturbed hierarchical LaplacianLω=LC(ω). We study the arithmetic means λ̅(ω) of theLω-eigenvalues. Under certain assumptions the normalized arithmetic means (λ̅−Eλ̅) ∕ σ(λ̅) converge in law to the standard normal distribution. In this note we study convergence in the total variation distance and estimate the rate of convergence.

Products of 2 × 2 stochastic matrices with random entries

1986 ◽  
Vol 23 (04) ◽  
pp. 1019-1024
Author(s):  
Walter Van Assche
Keyword(s):  
Rate Of Convergence ◽  
Beta Distribution ◽  
Stopping Time ◽  
Stochastic Matrices

The limit of a product of independent 2 × 2 stochastic matrices is given when the entries of the first column are independent and have the same symmetric beta distribution. The rate of convergence is considered by introducing a stopping time for which asymptotics are given.

scholarly journals Central and Local Limit Theorems for Numbers of the Tribonacci Triangle

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 880
Author(s):  
Igoris Belovas
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Normal Distribution ◽  
Rate Of Convergence ◽  
Limit Theorems ◽  
Local Limit Theorem ◽  
Local Limit ◽  
Constructive Proof ◽  
The Central Limit Theorem ◽  
Local Limit Theorems

In this research, we continue studying limit theorems for combinatorial numbers satisfying a class of triangular arrays. Using the general results of Hwang and Bender, we obtain a constructive proof of the central limit theorem, specifying the rate of convergence to the limiting (normal) distribution, as well as a new proof of the local limit theorem for the numbers of the tribonacci triangle.

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