Figure 9
Plot of expectation and standard deviation of particle numbers in subsystem changing with global density. (a) Expectation \(\langle {{\rm{n}}}_{{\rm{i}}}\rangle \). (b) Standard deviation \(\sqrt{{\rm{D}}\langle {{\rm{n}}}_{{\rm{i}}}\rangle /(K-1)}\). Lines depict analytical results. Scatters reflect Monte-Carlo simulations. Parameters are \(K=10,\,{\omega }_{1}^{u}=0.005,\,{\omega }_{1}^{d}=0.384\), \({\omega }_{2}^{u}=0.156,\,{\omega }_{2}^{d}=0.437,\,{\omega }_{3}^{u}=0.305\), \({\omega }_{3}^{d}=0.482,\,{\omega }_{4}^{u}=0.457,\,{\omega }_{4}^{d}=0.034\), \({\omega }_{5}^{u}=0.103,\,{\omega }_{5}^{d}=0.083,\,{\omega }_{6}^{u}=0.254\), \({\omega }_{6}^{d}=0.136,\,{\omega }_{7}^{u}=0.404,\)\({\omega }_{7}^{d}=0.187\), \({\omega }_{8}^{u}=0.056,\,{\omega }_{8}^{d}=0.233,\,{\omega }_{9}^{u}=0.208\), \({\omega }_{9}^{d}=0.285,\,{\omega }_{10}^{u}=0.359\) and \({\omega }_{10}^{d}=0.335\).
