Professor of Applied Mathematics
Email: gychen at math dot nctu dot edu dot tw Tel: 886-3-5712121 ext. 56421 Fax: 886-3-5724679 Address:
- Fall 2022¡G
- Calculus (I)
- Markov chains and mixing times
- Spring 2021¡G
- Calculus (II)
- Stochastic processes
- Ph.D. in Mathematics, Cornell University (2006)
- Research Area
- Probability Theory
- Stochastic Processes
- Academic Experience and Honors
- Eleanor Norton York Award for outstanding graduate students among Cornell mathematics graduate students(2005)
- Liu Memorial Award for demonstrated outstanding academic ability and performance among Cornell graduate students of Chinese descent(2006)
- Visiting Assistant Professor, National Center for Theoretical Science, Taiwan (2006/8 ~ 2007/7)
- Assistant Professor, Dept. of Applied Mathematics, National Chiao Tung University, Taiwan (2007/8 ~ 2011/7)
- Associate Professor, Dept. of Applied Mathematics, National Chiao Tung University, Taiwan (2011/8 ~2018/7)
- Professor, Dept. of Applied Mathematics, National Chiao Tung University, Taiwan (2018/8 ~2021/1)
- Professor, Dept. of Applied Mathematics, National Yang Ming Chiao Tung University, Taiwan (2021/2~)
- Young Theorist Award of NCTS (2008)
- Award for Junior Research Investigators, College of Science, NCTU (2009)
- NCTU Outstanding Teaching Award (2011), Excellent Teaching Award (2015)
- TMS Young Mathematician Award (2011)
- MOST Ta-You Wu Memorial Award (2014)
The Markov chain Monte Carlo (briefly, MCMC) method is a well-designed algorithm in sampling probability measures on discrete sets. Along with the Metropolis-Hasting algorithm, one may implement the MCMC method only with the local information of the targeted distributions, say the relative ratio, but without the information of the normalizing constant. When the MCMC method is simulated, it is important to select a (deterministic or random) time, say T, to stop the algorithm for sampling. Theoretically, the stopping time T can be the mixing time or the coupling time but none of them is easy to achieve.
The cutoff phenomenon is a phase-transit phenomenon in the evolution of Markov chains. This concept was introduced by Aldous and Diaconis in early 1980sin order to catch up the observation that the distribution of Markov chain is far from its stationarity before a time S and, after a relatively short period compared with S, the distribution turns out to be almost the limiting distribution. When a cutoff exists in a MCMC algorithm, the time S can be a good candidate for the stopping time of algorithm.
The MCMC method arises in many disciplines including the statistic physics, computer science, molecular biology, mathematical finance and more. From the viewpoint of interdisciplinary research, the underlying machinery can be very complicated, e.g. random walks on disordered random media and Markov processes on compact Riemannian manifolds, and a quick formula on the stopping time T and the cutoff time S will be very challenging but highly expected.Publications
- Guan-Yu Chen and Yuan-Chung Sheu, On the log-Sobolev constant for the simple random walk on the n-cycle: the even cases. J. Funct. Anal. 202 (2003), 473--485.
- Guan-Yu Chen, Ken Palmer and Yuan-Chung Sheu, The least cost super replicating portfolio for short puts and calls in the Boyle-Vorst model with transaction costs. Advances in Quantitative Analysis of Finance and Accounting Vol. 5 (2007), 1--22.
- Guan-Yu Chen, Ken Palmer and Yuan-Chung Sheu The least cost super replication portfolio in the Boyle-Vorst model with transaction costs. Accepted by International Journal of Theoretical and Applied Finance Vol. 11, No. 1 (2008), 55-85.
- Guan-Yu Chen and Laurent Saloff-Coste The cutoff phenomenon for randomized riffle shuffle. Random Structures and Algorithms 32 (2008), no. 3, 346--374.
- Guan-Yu Chen, Wai-Wai Liu and Laurent Saloff-Coste The logarithmic Sobolev constant of some finite Markov chains. Annales de la Faculte des Sciences de Toulouse Vol. XVII, No. 2 (2008), 239--290.
- Guan-Yu Chen and Laurent Saloff-Coste, The cutoff phenomenon for ergodic Markov processes. Electronic Journal of Probability, 13 (2008), 26--78.
- Guan-Yu Chen and Laurent Saloff-Coste, The L2-cutoff for reversible Markov processes. J. Funct. Anal. 258 (2010), 2246-2315.
- Guan-Yu Chen, Yang-Jen Fang and Yuan-Chung Sheu, The cutoff phenomenon for Ehrenfest chains. Stochastic Processes and their Applications, 122 (2012), 2830--2853.
- Guan-Yu Chen and Laurent Saloff-Coste, On the mixing time and spectral gap for birth and death chains. ALEA, Lat. Am. J. Probab. Math. Stat. Volume 10, Number 1 (2013), 293-321. arXiv:1304.4346
- Guan-Yu Chen and Laurent Saloff-Coste, Comparison of cutoffs between lazy walks and Markovian semigroups. J. Appl. Probab. Volume 50, Number 4 (2013), 943-959. arXiv:1304.4587
- Guan-Yu Chen and Laurent Saloff-Coste, Spectral computation for birth and death chains. Stochastic Processes and their Applications, 124 (2014), 848-882. arXiv:1305.0353
- Guan-Yu Chen and Laurent Saloff-Coste, Computing cutoff times for birth and death chains. Electronic Journal of Probability, 20 (2015), no. 76, 1-47. arXiv:1502.00361
- Guan-Yu Chen, Jui-Ming Hsu and Yuan-Chung Sheu, The L2-cutoff for reversible Markov chains, Annals of Applied Probability, 27 (2017), no. 4, 2305-2341.arXiv:1701.06663.
- Guan-Yu Chen and Takashi Kumagai, Cutoffs for product chains. Stochastic Processes and their Applications, 128 (2018), no. 11, 3840-3879. arXiv:1701.06665.
- Guan-Yu Chen and Takashi Kumagai, Products of random walks on finite groups with moderate growth. Tohoku Mathematical Journal, 71 (2019), no. 2, 281-302. arXiv:1703.05466.
Last modified date:2022/6/5