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  • 0 posts edited
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  • 71 votes cast
Aug
5
comment Least expensive way to “walk” with a convex potential
I imagine that it should be true but I would like to prove or disprove it.
Aug
5
comment Least expensive way to “walk” with a convex potential
I solved such a contradiction in the edit.
Aug
5
revised Least expensive way to “walk” with a convex potential
deleted 108 characters in body
Aug
4
revised Least expensive way to “walk” with a convex potential
edited body
Aug
4
comment Least expensive way to “walk” with a convex potential
I modified the statement. By convexity one could check that, if one takes two sequences, $r$, $r^{\prime}$ such that for every interval $[r_{i-1}, r_{i}]$ there exists a $j$ such that $[r_{i-1}, r_{i}] \subset [r^{\prime}_{j-1}, r^{\prime}_{j}]$, then $\mathcal{H}(r) \leq \mathcal{H}(r^{\prime})$. How to prove that the minimum is attained wen the jump lengths is the smallest as possible?
Aug
4
revised Least expensive way to “walk” with a convex potential
added 23 characters in body
Aug
4
revised Least expensive way to “walk” with a convex potential
added 9 characters in body
Aug
4
comment Convexity increases the “cost” of long steps
A related question... math.stackexchange.com/questions/1383894/…
Aug
4
asked Least expensive way to “walk” with a convex potential
Aug
1
comment Convexity increases the “cost” of long steps
I think that the condition that I needed in order the statement to be true is that, for each $[r^{\prime}_i, r^{\prime}_{i+1}]$, there exists and $i$ such that $[r^{\prime}_i, r^{\prime}_{i+1}] \subset [r_i, r_{i+1}] $.
Aug
1
accepted Convexity increases the “cost” of long steps
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.