On the diffusion geometry of graph Laplacians and applications

Applied and Computational Harmonic Analysis - Tập 46 - Trang 674-688 - 2019
Xiuyuan Cheng1, Manas Rachh1, Stefan Steinerberger2
1Applied Mathematics Program, Yale University, New Haven, CT 06510, USA
2Department of Mathematics, Yale University, New Haven, CT 06510, USA

Tài liệu tham khảo

Arnold, 2016, Effective confining potential of quantum states in disordered media, Phys. Rev. Lett., 116, 10.1103/PhysRevLett.116.056602 Banuelos, 1999, On the ‘hot spots’ conjecture of J. Rauch, J. Funct. Anal., 164, 1, 10.1006/jfan.1999.3397 Banuelos, 1994, Brownian motion and the fundamental frequency of a drum, Duke Math. J., 75, 575, 10.1215/S0012-7094-94-07517-0 Bonacich, 1972, Factoring and weighting approaches to status scores and clique identification, J. Math. Sociol., 2, 113, 10.1080/0022250X.1972.9989806 Bovier, 2002, Metastability and low lying spectra in reversible Markov chains, Comm. Math. Phys., 228, 219, 10.1007/s002200200609 Bovier, 2004, Metastability in reversible diffusion processes. I. Sharp asymptotics for capacities and exit times, J. Eur. Math. Soc. (JEMS), 6, 399, 10.4171/JEMS/14 Bovier, 2005, Metastability in reversible diffusion processes. II. Precise asymptotics for small eigenvalues, J. Eur. Math. Soc. (JEMS), 7, 69, 10.4171/JEMS/22 Burdzy, 1999, A counterexample to the “hot spots” conjecture, Ann. of Math. (2), 149, 309, 10.2307/121027 Dyer, 1991, Computing the Volume of Convex Bodies: A Case Where Randomness Provably Helps, vol. 44 Filoche, 2012, Universal mechanism for Anderson and weak localization, Proc. Natl. Acad. Sci. USA, 109, 14761, 10.1073/pnas.1120432109 Gavish, 2013, Normalized cuts are approximately inverse exit times, SIAM J. Matrix Anal. Appl., 34, 757, 10.1137/110826928 Georgiev Hsu, 1985, Probabilistic approach to the Neumann problem, Comm. Pure Appl. Math., 38, 445, 10.1002/cpa.3160380406 Levin, 2009 Meila, 2001 Melas, 1992, On the nodal line of the second eigenfunction of the Laplacian in R2, J. Differential Geom., 35, 255, 10.4310/jdg/1214447811 Ng, 2002, On spectral clustering: analysis and an algorithm, vol. 14 Payne, 1967, Isoperimetric inequalities and their applications, SIAM Rev., 9, 453, 10.1137/1009070 Rachh Steinerberger, 2014, Lower bounds on nodal sets of eigenfunctions via the heat flow, Comm. Partial Differential Equations, 39, 2240, 10.1080/03605302.2014.942739 Steinerberger, 2015, Sharp L1-Poincaré inequalities correspond to optimal hypersurface cuts, Arch. Math., 105, 179, 10.1007/s00013-015-0778-x Steinerberger, 2017, Localization of quantum states and landscape functions, Proc. Amer. Math. Soc., 145, 2895, 10.1090/proc/13343