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If i was to give an $n×n$ grid with each grid point having probability $p$ of being selected, would it be difficult to calculate distributions of various measures regarding the convex hull of all sele …

I've searched the web now for ages to try and find a paper on the asymptotic distribution of the area of the union of randomly placed discs on the plane. Ideally, I would be looking for the discs to b …

If I give a finite region of $\mathbb{R}^{2}$ and place $k$ circles of radius $r(k)$ uniformly at random inside, are there any known results for the probability that the circles do not overlap? Equiva …

I'm interested in what research has already been done with regards to the statistics of random voronoi diagrams. I have had a look on google scholar and results are a little inconclusive. I'm interest …

This is my second question about Random Voronoi diagrams, in my first question was given some excellent advice but i was not clear in explaining what i was looking for. I'm interested to know whethe …

I have the following problem consider a random bipartite with vertex classes $A$ and $B$ of size $|A|=|B|=\mathrm{log}^{2}(n)$ graph in which every possible edge is chosen independently with probabi …

Consider the random bipartite graph with vertex classes of size $n$ and each edge being present independently with probability $p(n)$. I know one way to prove the threshold of a perfect matching is t …

I'm reading the following paper http://www2.stat.duke.edu/~scs/Courses/Stat376/Papers/GibbsFieldEst/BesagJRSSB1974.pdf On page 7 they give the result that $$Q(\textbf{x}) = \sum_{1 \leq i \leq n} x_iG …

I'm looking at a random bipartite graph $K_{\omega(n)}*K_{\omega(n)}$ where $\mathrm{log}(n)\leq \omega(n) \leq n^{1/2}$, in which each of the $\omega(n)^{2}$ edges is placed randomly with probability …

I've been told recently that it's better i just for help regarding my 'specific' problem rather than lots of little questions around the same topic which appear somewhat unclear. I would first like to …

Consider a random bipartite graph constructed on vertex classes of size $n$ with each edge present independently with probability $p$. How could I go about calculating the size of the expected matchin …