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The study of physical systems using probabilistic reasoning, especially relating small-scale classical mechanics to large-scale thermodynamics.

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Signs of Kravchuk matrix asymptotically produce a large circular region with hyperbolic sink...

The Kravchuk matrix of dimension $n+1$ is such that its entries satisfy $$K_{i,j}^{(n+1)}=[x^i](1+x)^{n-j}(1-x)^j\quad\forall0\le i,j\le n.$$ It enjoys properties such as involution and has various ex …
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