An excited random walk (ERW) is a self-interacting non-Markovian random walk in
which the future behavior of the walk is influenced by the number of times the walk
has previously visited its current site. We study the speed of the walk, defined as
, where
is the state of
the walk at time .
While results exist that indicate when the speed is nonzero, there exists no explicit
formula for the speed. It is difficult to solve for the speed directly due to complex
dependencies in the walk since the next step of the walker depends on how many
times the walker has reached the current site. We derive the first nontrivial upper
and lower bounds for the speed of the walk. In certain cases these upper and lower
bounds are remarkably close together.
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