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  • 0 posts edited
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  • 70 votes cast
Jul
21
revised Probability of random walk visit in nonameanable graphs
edited title
Jul
21
asked Probability of random walk visit in nonameanable graphs
Jul
20
revised Convexity increases the “cost” of long steps
added 268 characters in body
Jul
20
revised Convexity increases the “cost” of long steps
added 10 characters in body
Jul
20
asked Convexity increases the “cost” of long steps
Jul
18
comment subadditivity for sets and monotonic function
Outer boundary would be the set of sites which have a neighbour in the set but which are not contained in the set.
Jul
18
comment subadditivity for sets and monotonic function
Sorry. I meant "connected"…. problems with my English :)
Jul
18
revised Covering a family of sets of $\mathbb{Z}^d$ with boxes of a given diameter
added 3 characters in body
Jul
18
comment subadditivity for sets and monotonic function
Perhaps compactness is not even necessary.
Jul
18
comment subadditivity for sets and monotonic function
I understand, thanks. Hence, consider all sequences $( A_n )$ such that: (1) $A_n$ is a compact set (2) the function $f$ is sub additive and translation invariant (3) $\limsup\limits_{n \rightarrow \infty} \frac{|\partial A_n|}{|A_n|} = 0$, where $\partial A_n$ is the outer boundary of $A_n$. I believe that the limit for all these sequences is the same.
Jul
17
comment Covering a family of sets of $\mathbb{Z}^d$ with boxes of a given diameter
The value $\eta$ might depend on $d$.
Jul
17
asked Covering a family of sets of $\mathbb{Z}^d$ with boxes of a given diameter
Jul
17
comment subadditivity for sets and monotonic function
If additionally we require translation invariance, i.e. for any $A \subset \mathbb{Z}^d$, $x \in \mathbb{Z}^d$, then $f(A + x) = f(A)$, is the limit the same for any increasing sequence?
Jul
17
accepted Limit of continuous convex functions.
Jul
17
asked Limit of continuous convex functions.
Jul
16
accepted subadditivity for sets and monotonic function
Jul
16
comment subadditivity for sets and monotonic function
I understand, thanks. What additional assumption should $f$ satisfy in order the limit to exist?
Jul
16
comment subadditivity for sets and monotonic function
I added an edit that modifies a bit the question.
Jul
16
revised subadditivity for sets and monotonic function
The assumption of increasing sequence has been added.
Jul
16
revised subadditivity for sets and monotonic function
added 16 characters in body