We consider the nearest-neighbor model on the finite tree T with generator L. We obtain a twosided estimate of the spectral gap by factor 2. We also identify explicitly the Lipschitzian norm of the operator(-L)^(-1) i...We consider the nearest-neighbor model on the finite tree T with generator L. We obtain a twosided estimate of the spectral gap by factor 2. We also identify explicitly the Lipschitzian norm of the operator(-L)^(-1) in propriate functional space. This leads to the identification of the best constant in the generalized Cheeger isoperimetric inequality on the tree, and to transportation-information inequalities.展开更多
基金National Natural Science Foundation of China (Grant Nos. 11271294, 11101040, 11431014 and 11371283)Beijing Youth Excellent Talents Program (Grant No. 0264)+1 种基金National Creative Group under Beijing Normal University 985 Projectsthe Fundamental Research Funds for the Central Universities and le Project ANR EVOL
文摘We consider the nearest-neighbor model on the finite tree T with generator L. We obtain a twosided estimate of the spectral gap by factor 2. We also identify explicitly the Lipschitzian norm of the operator(-L)^(-1) in propriate functional space. This leads to the identification of the best constant in the generalized Cheeger isoperimetric inequality on the tree, and to transportation-information inequalities.
