Correlation Inequalities for Interacting Particle Systems with Duality
Correlation Inequalities for Interacting Particle Systems with Duality
复制标题
DOI：
10.1007/s10955-010-0055-0
复制
发表时间：
2010-09
影响因子：
1.6
通讯作者：
C. Giardinà;F. Redig;K. Vafayi
中科院分区：
文献类型：
--
作者：
C. Giardinà;F. Redig;K. Vafayi
我们证明了一个独立的随机游走系统和一个随机游走系统之间的一个不平等性，该系统要么相互吸引-一个过程，我们在这里称之为对称包含过程（SIP）-或相互排斥-一个广义版本的著名的对称排斥过程。作为应用，我们得到了SIP以及一些用作热传导模型的相互作用扩散（即所谓的布朗动量过程和布朗能量过程）的新的相关不等式。这些不等式是对称排斥过程的不等式（在相反的方向上）的对应物，表明SIP是对称排斥过程的自然玻色子模拟，这是费米子的。最后，我们考虑一个边界驱动的版本的SIP，我们证明了对偶，然后得到相关不等式。
We prove acomparison inequalitybetween a system of independent random walkers and a system of random walkers which either interact byattracting each other—a process which we call here the symmetric inclusion process (SIP)—orrepel each other—a generalized version of the well-known symmetric exclusion process. As an application, newcorrelation inequalitiesare obtained for the SIP, as well as for some interacting diffusions which are used as models of heat conduction,—the so-called Brownian momentum process, and the Brownian energy process. These inequalities are counterparts of the inequalities (in the opposite direction) for the symmetric exclusion process, showing that the SIP is a natural bosonic analogue of the symmetric exclusion process, which is fermionic. Finally, we consider a boundary driven version of the SIP for which we prove duality and then obtain correlation inequalities.