1,243 reputation
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bio website perso.ens-lyon.fr/…
location Lyon
age 37
visits member for 4 years, 1 month
seen yesterday

Sep
22
awarded  Yearling
Sep
13
comment Can we give any upper bound on $E[\max_{n \leq N} X_n]$ in terms of $\max_{n \leq N} E[X_n]$
Another counterexample: take $(X_n)$ iid of mean $0$, then $\max E[X_n] = 0$. But $E[\max X_n]$ can take pretty much any value; if the support of the distribution of $X$ is not bounded above, then as $N \to \infty$ it also goes to $+\infty$.
Sep
8
comment First passage percolation on a random geometric graph in the large connectivity limit
It should not be difficult to show that $h_\infty$ does not depend on the distribution as soon as $P$ has positive density and no atom at $0$: indeed, as soon as bonds with small weight percolate "enough", they should be the only ones present on the shortest path, at least asymptotically as $\rho\to\infty$.
Sep
8
comment First passage percolation on a random geometric graph in the large connectivity limit
Do you expect the underlying point process model to be relevant? Or would you think that something similar could happen e.g. for FPP on the square lattice?
Mar
19
comment Pairs of Permutations up to Simultaneous Conjugation
(2 years later) Is there an efficient algorithmic way to check if two pairs of permutations are simultaneously conjugated like this?
Nov
7
comment Embedding points in 2D based on distance estimates?
I believe fdp and sfdp implement something like that, where by default $l_{ij}=1$ but you can specify a length for an edge to set another value.
Sep
22
awarded  Yearling
Sep
18
answered Embedding points in 2D based on distance estimates?
Aug
16
answered Estimate size of graph by taking random walks
Jun
11
answered Conway's game of life for random initial position
Jun
11
comment Conway's game of life for random initial position
@helper Sure, I did say "there may be", and it is quite possible that indeed density would always go to zero. I was simply pointing out that what you said could not be enough, because it did not use the specifics of GoL. And in general it is quite hard to tell what happens for a given model ...
Jun
11
comment Conway's game of life for random initial position
@helper To give a more "physical" intuition: the time needed for a box to die out will typically be exponential in the volume of the box (that's what it takes for each cell to die at the same time), while the time for a neighbouring box to make you alive again is linear in the diameter (propagation fronts move linearly). So even if one of the regions were to die out (which it will), there may be plenty of "life reservoirs" in the vicinity to resuscitate it before they themselves die.
Jun
11
comment Conway's game of life for random initial position
@helper The argument is definitely wrong. There are processes (e.g. the contact process with high enough propagation rate, or "slices" of directed percolation) which die in any finite volume for the reason you mention, but nevertheless admit invariant distributions with positive asymptotic density.
May
24
answered Independence using reflecting brownian motion
May
24
comment Independence using reflecting brownian motion
Wait, if you take 2d Brownian motion conditioned on the event that at time 1 its two coordinates have the same sign, or equivalently if you take two independent Brownian motions $B_1$ and $B_2$ and then set $X=B_1$ and $Y=\pm B_2$ where the sign is chosen so that $X$ and $Y$ have the same sign at time $1$, then $X$ and $Y$ have independent absolute values but are not independent...
May
15
comment Another colored balls puzzle (part II)
Good to know, at least my asymptotic analysis gives the right order of magnitude and even the right growth rate. Far from an exact result, but I believe that the approach is more robust than bijective methods like the one suggested by Ori.
May
15
revised Another colored balls puzzle (part II)
Result of the computation for case 1
May
15
comment Another colored balls puzzle (part II)
Very nice indeed!
May
14
comment Another colored balls puzzle (part II)
(Actually case 1 needs a proper estimate for the exponential rate, which I don't have time to do right now but should be straightforward enough ... sorry ...)
May
14
answered Another colored balls puzzle (part II)