Vincent Beffara
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 Sep 22 awarded Yearling Jul 31 answered Number of samples needed as input to Bernoulli factory Jul 17 answered Reflection “monotonicity” of two point function percolation Apr 15 answered Area enclosed by Brownian motion (without winding number) Feb 6 answered Statistics of strongly connected components in random directed graphs Feb 6 comment Statistics of strongly connected components in random directed graphs What exactly do you mean by "non-extreme values of $p$"? For fixed $p\in(0,1)$ and $N\to\infty$ there will still be a unique component w.h.p. ... Dec 7 answered Probability that a self-avoiding walk on $\mathbb{Z}^3$ closes to a polygon Nov 2 comment When exactly and why matrix multiplication became a part of undergraduate curriculum? Well line 2 is the product. 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.