We introduce a method for studying monotonicity of the speed of excited random walks in high dimensions, based on a formula for the speed obtained via cut-times and Girsanov's transform. While the method gives rise to similar results as have been or can be obtained via the expansion method of van der Hofstad and Holmes, it may be more palatable to a general probabilistic audience. We also revisit the law of large numbers for stationary cookie environments. In particular, we introduce a new notion of $e_1-$exchangeable cookie environment and prove the law of large numbers for this case.
展开▼
机译：我们介绍一种研究高尺寸激发随机行走速度的单调性的方法，基于通过切换时间和Girsanov的变换获得的速度的公式。虽然该方法产生类似的结果，但通过van der Hofstad和Holmes的扩展方法可以获得或可以获得，而这可能对一般概率观众更加卑鄙。我们还重新审视了固定饼干环境的大量规定。特别是，我们介绍了$ E_1-$兑换饼干环境的新概念，并为这种情况证明了大量的法律。
展开▼
