# On a lower bound for the Chung–Diaconis–Graham random process

@article{Hildebrand2019OnAL,
title={On a lower bound for the Chung–Diaconis–Graham random process},
author={Martin Hildebrand},
journal={Statistics \& Probability Letters},
year={2019}
}
• M. Hildebrand
• Published 1 September 2019
• Mathematics
• Statistics & Probability Letters
4 Citations
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## References

SHOWING 1-8 OF 8 REFERENCES
A lower bound for the Chung-Diaconis-Graham random process
Chung, Diaconis, and Graham considered random processes of the form X n+1 = a n X n + b n (mod p) where p is odd, X 0 = 0, an = 2 always, and b n are i.i.d. for n = 0, 1, 2,.... In this paper, we
On the Chung-Diaconis-Graham random process
Chung, Diaconis, and Graham considered random processes of the form $X_{n+1}=2X_n+b_n \pmod p$ where $X_0=0$, $p$ is odd, and $b_n$ for $n=0,1,2,\dots$ are i.i.d. random variables on $\{-1,0,1\}$. If
A Birthday Paradox for Markov Chains, with an Optimal Bound for Collision in the Pollard Rho Algorithm for Discrete Logarithm
• Mathematics, Computer Science
ANTS
• 2008
This is the first proof of the correct bound which does not assume every step of the algorithm produces an i.i.d. sample from G and it is shown that with high probability a collision occurs in Θ(√|G|)steps.
Random Walks Arising in Random Number Generation
• Mathematics
• 1987
On considere la forme generale des generateurs de nombres aleatoires X n+1 =aX n +b(mod. p). Differents schemas existent pour combiner ces generateurs. Dans un schema, a et b sont eux-memes choisis
An Introduction to Probability Theory and Its Applications
Thank you for reading an introduction to probability theory and its applications vol 2. As you may know, people have look numerous times for their favorite novels like this an introduction to
• 2011
• 1968