Large deviations and wandering exponent for random walk in a dynamic beta environment
Large deviations and wandering exponent for random walk in a dynamic beta environment
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DOI：
10.1214/18-aop1306
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发表时间：
2018-01
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影响因子：
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通讯作者：
M. Bal'azs;F. Rassoul-Agha;T. Seppalainen
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文献类型：
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作者：
M. Bal'azs;F. Rassoul-Agha;T. Seppalainen
动态独立同分布中的随机游动。β随机环境，以非典型速度逃逸为条件，收敛到原始行走的Doob变换。Doob变换的环境在时间上是相关的，i.i.d.它的边际密度函数是贝塔密度和超几何函数的乘积。在其平均分布下，变换行走服从游荡指数2/3，符合Kardar-Parisi-Zhang普适性. Doob变换中的调和函数来自Busemann型极限，并且在淬火大偏差率函数的变分问题中作为极值出现。
Random walk in a dynamic i.i.d. beta random environment, conditioned to escape at an atypical velocity, converges to a Doob transform of the original walk. The Doob-transformed environment is correlated in time, i.i.d. in space, and its marginal density function is a product of a beta density and a hypergeometric function. Under its averaged distribution the transformed walk obeys the wandering exponent 2/3 that agrees with Kardar-Parisi-Zhang universality. The harmonic function in the Doob transform comes from a Busemann-type limit and appears as an extremal in a variational problem for the quenched large deviation rate function.