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- W2000119783 abstract "Let $omega = (p_x)_{xinmathbb{Z}}$ be an i.i.d. collection of (0, 1)-valued random variables. Given $omega$, let $(X_n)_{n geq 0}$ be the Markov chain on $mathbb{Z}$ defined by $X_0 = 0$ and $X_{n + 1} = X_n + 1(operatorname{resp}. X_n - 1)$ with probability $p_{X_n}(operatorname{resp}.1 - p_{X_n})$. It is shown that $X_n/n$ satisfies a large deviation principle with a continuous rate function, that is, $lim_{nrightarrowinfty}frac{1}{n}log P_omega(X_n = lfloortheta_nnrfloor) = -I(theta) omega-mathrm{a.s.}text{for} theta_nrightarrowinlbrack -1, 1rbrack.$ First, we derive a representation of the rate function $I$ in terms of a variational problem. Second, we solve the latter explicitly in terms of random continued fractions. This leads to a classification and qualitative description of the shape of $I$. In the recurrent case $I$ is nonanalytic at $theta = 0$. In the transient case $I$ is nonanalytic at $theta = -theta_c, 0, theta_c$ for some $theta_c geq 0$, with linear pieces in between." @default.
- W2000119783 created "2016-06-24" @default.
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- W2000119783 date "1994-07-01" @default.
- W2000119783 modified "2023-10-18" @default.
- W2000119783 title "Large Deviations for a Random Walk in Random Environment" @default.
- W2000119783 doi "https://doi.org/10.1214/aop/1176988607" @default.
- W2000119783 hasPublicationYear "1994" @default.
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