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Amir Sagiv
Amir Sagiv
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For a symmetric Symmetric random walk $S_n$, if we have a bound $P(S_n \in A) < \delta$, do we get a boundwalks - bounds on the amount of time $S_n$ spendsspent in a subset $A$?

For a symmetric random walk $S_n$, if we have a bound $P(S_n \in A) < \delta$, do we get a bound on the amount of time $S_n$ spends in $A$?

Let $S_n$ be a symmetric random walk on the integers. Let $A$ be a subset of bounded upper density with a bound $P(S_n \in A) < \delta(\epsilon)$. Do we get a bound like $P\left(\frac{\#\{n = 1, \cdots, N \mid S_n \in A\}}{N} > \epsilon \right) < \epsilon$?

For a symmetric random walk $S_n$, if we have a bound $P(S_n \in A) < \delta$, do we get a bound on the amount of time $S_n$ spends in $A$?

Let $S_n$ be a symmetric random walk on the integers. Let $A$ be a subset of bounded upper density with a bound $P(S_n \in A) < \delta(\epsilon)$. Do we get a bound like $P\left(\frac{\#\{n = 1, \cdots, N \mid S_n \in A\}}{N} > \epsilon \right) < \epsilon$?

Symmetric random walks - bounds on the amount of time spent in a subset $A$?

For a symmetric random walk $S_n$, if we have a bound $P(S_n \in A) < \delta$, do we get a bound on the amount of time $S_n$ spends in $A$?

Let $S_n$ be a symmetric random walk on the integers. Let $A$ be a subset of bounded upper density with a bound $P(S_n \in A) < \delta(\epsilon)$. Do we get a bound like $P\left(\frac{\#\{n = 1, \cdots, N \mid S_n \in A\}}{N} > \epsilon \right) < \epsilon$?

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user145350
user145350

For a symmetric random walk $S_n$, if we have a bound $P(S_n \in A) < \delta$, do we get a bound on the amount of time $S_n$ spends in $A$?

Let $S_n$ be a symmetric random walk on the integers. Let $A$ be a subset of bounded upper density with a bound $P(S_n \in A) < \delta(\epsilon)$. Do we get a bound like $P\left(\frac{\#\{n = 1, \cdots, N \mid S_n \in A\}}{N} > \epsilon \right) < \epsilon$?