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We introduce a new interacting particles model with blocking and pushing interactions. Particles evolve on the positive line jumping on their own volition rightwards or leftwards according to geometric jumps with parameter q. We show that the model involves a Pieri-type formula for the orthogonal group. We prove that the two extreme cases - q=0 and q=1 - lead respectively to a random tiling model studied by Borodin and Kuan and to a random matrix model.
We have introduced recently a particles model with blocking and pushing interactions which is related to a Pieri type formula for the orthogonal group. This model has a symplectic version presented here.
The Skorokhod map is a convenient tool for constructing solutions to stochastic differential equations with reflecting boundary conditions. In this work, an explicit formula for the Skorokhod map $Gamma_{0,a}$ on $[0,a]$ for any $a>0$ is derived. Spe
We study the spectrum reconstruction technique. As is known to all, eigenvalues play an important role in many research fields and are foundation to many practical techniques such like PCA(Principal Component Analysis). We believe that related algori
Elaborating on the model from voter process with mixed-mechanism under suitable scaling, I have two new mechanisms which are random switch and unbiased local Homogenization and subtly biased advantage but with state dependent coefficient involved. Th
We provide a new tableau model from which one can easily deduce the characters of irreducible polynomial representations of the orthogonal group $mathrm{O}_n(mathbb{C})$. This model originates from representation theory of the $imath$quantum group of