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- W2953240286 abstract "Let $T_{n,m}=mathbb Z_ntimesmathbb Z_m$, and define a random mapping $phicolon T_{n,m}to T_{n,m}$ by $phi(x,y)=(x+1,y)$ or $(x,y+1)$ independently over $x$ and $y$ and with equal probability. We study the orbit structure of such ``quenched random walks'' $phi$ in the limit $m,ntoinfty$, and show how it depends sensitively on the ratio $m/n$. For $m/n$ near a rational $p/q$, we show that there are likely to be on the order of $sqrt{n}$ cycles, each of length O(n), whereas for $m/n$ far from any rational with small denominator, there are a bounded number of cycles, and for typical $m/n$ each cycle has length on the order of $n^{4/3}$." @default.
- W2953240286 created "2019-06-27" @default.
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- W2953240286 date "2008-06-06" @default.
- W2953240286 modified "2023-09-23" @default.
- W2953240286 title "Monotone loop models and rational resonance" @default.
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