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- W4226220424 abstract "Given a transition matrix $P$ indexed by a finite set $V$ of vertices, the voter model is a discrete-time Markov chain in ${0,1}^V$ where at each time-step a randomly chosen vertex $x$ imitates the opinion of vertex $y$ with probability $P(x,y)$. The noisy voter model is a variation of the voter model in which vertices may change their opinions by the action of an external noise. The strength of this noise is measured by an extra parameter $p in [0,1]$. The noisy voter model is a Markov chain with state space ${0,1}^V$, and has a unique stationary distribution $Gamma$ when $p > 0$. In this paper, we study $Gamma$ when the number of vertices in $V$ tends to infinity. In particular we analyse the random variable $S = sum_{x in V}pi(x)xi(x)$, where $pi$ is the stationary distribution of the transition matrix $P$, and $xi in {0,1}$ is sampled from $Gamma$. Allowing $P$ and $p$ to be functions of the size $|V|$, we show that, under appropriate conditions, a normalised version of $S$ converges to a Gaussian random variable. We provide further analysis of the noisy voter model on a variety of graphs including the complete graph, cycle, torus and hypercube." @default.
- W4226220424 created "2022-05-05" @default.
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- W4226220424 date "2021-12-02" @default.
- W4226220424 modified "2023-09-29" @default.
- W4226220424 title "On the stationary distribution of the noisy voter model" @default.
- W4226220424 hasPublicationYear "2021" @default.
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