39 citations · 67 across the 5 of their papers we have counts for
8 papers
Excited Random Walk in a Markovian Environment
Nicholas Travers
One dimensional excited random walk has been extensively studied for bounded, i.i.d. cookie environments. In this case, many important properties of the walk including transience o…
Transience, Recurrence and the Speed of a Random Walk in a Site-Based Feedback Environment
Ross G. Pinsky, Nicholas F. Travers
We study a random walk on which evolves in a dynamic environment determined by its own trajectory. Sites flip back and forth between two modes, and . consec…
Inversions and Longest Increasing Subsequence for -Card-Minimum Random Permutations
Nicholas F. Travers
A random -permutation may be generated by sequentially removing random cards from an -card deck . The permutation is simply the sequence of…
Exponential Bounds for Convergence of Entropy Rate Approximations in Hidden Markov Models Satisfying a Path-Mergeability Condition
Nicholas F. Travers
A hidden Markov model (HMM) is said to have path-mergeable states if for any two states i,j there exists a word w and state k such that it is possible to transition from both i and…
Infinite Excess Entropy Processes with Countable-State Generators
Nicholas F. Travers, James P. Crutchfield
We present two examples of finite-alphabet, infinite excess entropy processes generated by invariant hidden Markov models (HMMs) with countable state sets. The first, simpler examp…
Equivalence of History and Generator Epsilon-Machines
Nicholas F. Travers, James P. Crutchfield
Epsilon-machines are minimal, unifilar presentations of stationary stochastic processes. They were originally defined in the history machine sense, as hidden Markov models whose st…
Asymptotic Synchronization for Finite-State Sources
Nicholas F. Travers, James P. Crutchfield
We extend a recent synchronization analysis of exact finite-state sources to nonexact sources for which synchronization occurs only asymptotically. Although the proof methods are q…
Exact Synchronization for Finite-State Sources
Nicholas F. Travers, James P. Crutchfield
We analyze how an observer synchronizes to the internal state of a finite-state information source, using the epsilon-machine causal representation. Here, we treat the case of exac…