TY - JOUR
T1 - Lower bounds on partial sums of expected hitting times
AU - Yoon, Hyungkuk
AU - Kim, Bara
AU - Kim, Jeongsim
N1 - Funding Information:
B. Kim’s research was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) ( NRF-2017R1A2B4012676 ). J. Kim’s research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Korea ( 2017R1D1A1B03029542 ).
Publisher Copyright:
© 2020 Elsevier B.V.
PY - 2020/5
Y1 - 2020/5
N2 - We consider a simple random walk on a connected undirected graph with N vertices. Palacios (2010) and Palacios and Renom (2012) investigated lower bounds on partial sums of expected hitting times of the random walk. In this paper, we show that Palacios’ (2010) lower bound is the best for all multigraphs. In addition, we show that the conjecture made by Palacios and Renom (2012) for simple graphs is true for N≤5, but it is not true for N≥6.
AB - We consider a simple random walk on a connected undirected graph with N vertices. Palacios (2010) and Palacios and Renom (2012) investigated lower bounds on partial sums of expected hitting times of the random walk. In this paper, we show that Palacios’ (2010) lower bound is the best for all multigraphs. In addition, we show that the conjecture made by Palacios and Renom (2012) for simple graphs is true for N≤5, but it is not true for N≥6.
KW - Hitting times
KW - Random walks on graphs
UR - http://www.scopus.com/inward/record.url?scp=85078819982&partnerID=8YFLogxK
U2 - 10.1016/j.spl.2020.108715
DO - 10.1016/j.spl.2020.108715
M3 - Article
AN - SCOPUS:85078819982
VL - 160
JO - Statistics and Probability Letters
JF - Statistics and Probability Letters
SN - 0167-7152
M1 - 108715
ER -