任意图上KMP及其他随机交换模型的谱隙
Spectral gap of the KMP and other stochastic exchange models on arbitrary graphs
AI总结：
本文提出一种简单策略，为任意图上的KMP、调和过程及即时交换模型等可逆随机交换模型推导仅依赖最坏情形线性统计量和图无关动力学因子的普适谱隙上下界，并证明这些界在多个模型中精确甚至饱和为恒等式。
摘要：
我们提出一种简单策略，用于推导任意图上可逆随机交换模型谱隙的普适界。Kipnis-Marchioro-Presutti（KMP）模型、调和过程（HP）和即时交换模型（IEM）都属于这一类。我们的上界和下界仅依赖于两个特征：最坏情形线性统计量和一个本质上与图无关的动力学因子。对于上述三个例子，这些界是精确的，并且在某些对数凹区域中对HP和IEM甚至饱和为恒等式。该证明——即使在非可逆情形下也能给出特征值的界——关键地利用了这些模型特征结构的刚性以及最近在[DMFG24, GRT25]中引入的相应隐参数模型的定量收缩率。
英文摘要：
We present a simple strategy to derive universal bounds on the spectral gap of reversible stochastic exchange models on arbitrary graphs. The Kipnis-Marchioro-Presutti (KMP) model, the harmonic process (HP), and the immediate exchange model (IEM) are all examples that fall into this class. Our upper and lower bounds depend only on two features: worst-case linear statistics and a kinetic factor, which is, in essence, graph-independent. For the three aforementioned examples, these bounds are sharp, and even saturate to an identity for HP and IEM in some log-concave regimes. The proof -- which yields bounds for eigenvalues even in the non-reversible context -- crucially exploits the rigidity of the eigenstructure of these models and quantitative contraction rates of the corresponding hidden parameter models recently introduced in [DMFG24, GRT25].
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