Fukasawa, Masaaki Limit theorems for random walks under irregular conductance. (English) Zbl 1292.60097 Proc. Japan Acad., Ser. A 89, No. 8, 87-91 (2013). Summary: For a general one-dimensional random walk with state-dependent transition probabilities, we present weak limits of the empirical moments of conductance along the path of the random walk. In particular we obtain remarkably simple quenched convergences under random conductance model. MSC: 60K37 Processes in random environments 60F05 Central limit and other weak theorems Keywords:arc-sine law; empirical moment; random conductance; weak convergence × Cite Format Result Cite Review PDF Full Text: DOI Euclid References: [1] M. Biskup, Recent progress on the random conductance model, Probab. Surv. 8 (2011), 294-373. · Zbl 1245.60098 · doi:10.1214/11-PS190 [2] P. G. Doyle and L. Snell, Random walks and electric networks , Carus Mathematical Monographs, 22, Math. Assoc. America, Washington, DC, 1984. · Zbl 0583.60065 [3] M. Fukasawa and M. Rosenbaum, Central limit theorems for realized volatility under hitting times of an irregular grid, Stochastic Process. Appl. 122 (2012), no. 12, 3901-3920. · Zbl 1255.60034 · doi:10.1016/j.spa.2012.08.005 [4] V. Sidoravicius and A.-S. Sznitman, Quenched invariance principles for walks on clusters of percolation or among random conductances, Probab. Theory Related Fields 129 (2004), no. 2, 219-244. · Zbl 1070.60090 · doi:10.1007/s00440-004-0336-0 [5] S. Watanabe, Generalized arc-sine laws for one-dimensional diffusion processes and random walks, in Stochastic Analysis (Ithaca, NY, 1993) , 157-172, Proc. Sympos. Pure Math., 57 Amer. Math. Soc., Providence, RI, 1995. · Zbl 0824.60080 · doi:10.1090/pspum/057/1335470 [6] O. Zeitouni, Random walks in random environments, in Proceedings of the International Congress of Mathematicians, Vol. III (Beijing, 2002) , 117-127, Higher Ed. Press, Beijing, 2002. · Zbl 1007.60102 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.