Combinatorics of the quantum symmetric simple exclusion process, associahedra and free cumulants

IF 1.5 Q2 PHYSICS, MATHEMATICAL
P. Biane
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引用次数: 6

Abstract

The Quantum Symmetric Simple Exclusion Process (QSSEP) is a model of quantum particles hopping on a finite interval and satisfying the exclusion principle. Recently Bernard and Jin have studied the fluctuations of the invariant measure for this process, when the number of sites goes to infinity. These fluctuations are encoded into polynomials, for which they have given equations and proved that these equations determine the polynomials completely. In this paper, I give an explicit combinatorial formula for these polynomials, in terms of Schr\"oder trees. I also show that, quite surprisingly, these polynomials can be interpreted as free cumulants of a family of commuting random variables.
量子对称简单不相容过程的组合学,缔合面体和自由累积量
量子对称简单不相容过程(QSSEP)是量子粒子在有限区间上跳跃并满足不相容原理的模型。最近,Bernard和Jin研究了这一过程中,当点的数量趋于无穷大时,不变测度的波动。这些波动被编码成多项式,他们给出了多项式的方程,并证明了这些方程完全决定了多项式。在本文中,我给出了这些多项式的一个显式组合公式,用Schr\ o树表示。我还展示了,非常令人惊讶的是,这些多项式可以被解释为一组交换随机变量的自由累积量。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
CiteScore
2.30
自引率
0.00%
发文量
16
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