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• the general 3-particle system is constructed, with three couplings and one free function • higher-particle systems exist, tedious to construct; hypergeometric functions appear •
Considering one-dimensional (1D) quantum [1] and classical [2] Hamiltonians with polynomial ladder operators (i.e. polynomial in the momenta) satisfying a polynomial Heisenberg
Furthermore, we consider a stationary Hammersley process and use the previous results to show that trajectories of a second class particle and a dual second class particles touch
We begin by showing that (a) in equilibrium the total variation distance between the marginal distribution of a given queue length and the limiting distribution L λ,d is small; and
The historical tree of a particle present in the Marcus-Lushnikov process at a given time t encodes information about the times and masses of the coagulation events that have
In particular, we show that non-trivial correlation measures have unbounded support, and that Md has a certain convexity property.. Using this convexity property, we construct
There it has been shown that, under certain moment conditions, one can construct a k -dimensional random walk conditioned to stay in a strict order at all times.. Moreover, they
Abstract. We study an integrable case of n -particle Toda lattice: open chain with boundary terms containing 4 parameters. For this model we construct a B¨acklund transformation
