The unit square $I=[0,1]^2$ is divided into two rectangles by the vertical line $x=p$, where $p\in(0,1)$. Consider $N$ independent uniformly distributed points on $I$, which we interpret as a population of individuals, with the line $x=p$ representing a community boundary that separates the population into two communit...
It is proved that, as long as $p=o(\log n /n)$, for any $\varepsilon>0$, one can construct a confidence set of vertices of size $K(\varepsilon)$ that depends only on $\varepsilon$ and not on $n$, such that it contains the root with probability at least $1-\varepsilon$.
Luc Devroye, Gábor Lugosi, Neeladri Maitra· 1 citation· ⚡1
We consider multipartite random graphs with given degree sequences, within and across different partitions. Under general assumptions, we prove the local limit of this graph is a multi-type branching process, establish that a giant component exists only when the local limit survives, and deduce that the typical distanc...
Neeladri Maitra· 0 citations
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