## 4 Citations

Accelerating abelian random walks with hyperbolic dynamics

- MathematicsProbability Theory and Related Fields
- 2022

Given integers d ≥ 2 ,n ≥ 1 , we consider aﬃne random walks on torii ( Z / n Z ) d deﬁned as X t + 1 = AX t + B t mod n , where A ∈ GL d ( Z ) is a invertible matrix with integer entries and ( B t )…

Mixing time of the Chung–Diaconis–Graham random process

- Mathematics
- 2020

Define $$(X_n)$$ ( X n ) on $${\mathbf {Z}}/q{\mathbf {Z}}$$ Z / q Z by $$X_{n+1} = 2X_n + b_n$$ X n + 1 = 2 X n + b n , where the steps $$b_n$$ b n are chosen independently at random from $$-1, 0,…

Markov chains on finite fields with deterministic jumps

- MathematicsElectronic Journal of Probability
- 2022

We study the Markov chain on $\mathbf{F}_p$ obtained by applying a function $f$ and adding $\pm\gamma$ with equal probability. When $f$ is a linear function, this is the well-studied…

Cut-off phenomenon for the ax+b Markov chain over a finite field

- Mathematics
- 2019

We study the Markov chain $x_{n+1}=ax_n+b_n$ on a finite field $\mathbb{F}_p$, where $a \in \mathbb{F}_p$ is fixed and $b_n$ are independent and identically distributed random variables in…

## References

SHOWING 1-8 OF 8 REFERENCES

A lower bound for the Chung-Diaconis-Graham random process

- Mathematics
- 2008

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

- Mathematics
- 2005

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 ScienceANTS
- 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

- Mathematics
- 1950

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