Guan-Yu Chen(中文版)

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Assistant Professor of Applied Mathematics

Contact information Email: gychen@math.nctu.edu.tw Tel: 886-3-5712121 ext. 56421 Fax: 886-3-5724679 Address: Department of Applied Mathematics, National Chiao Tung University 1001 Ta Hsueh Road, Hsinchu 30050, Taiwan

Teaching

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• Spring 2010：
  • Advanced Calculus(II)
  • Stochastic Processes
• Fall 2009：
  • Advanced Calculus(I)

 
Curriculum Vitae

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• Education
  • 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 (2007/08 ~ )
  • Young Theorist Award of NCTS (2008)
  • Award for Junior Research Investigators, College of Science, NCTU (2009)
    

Research Interests

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I am interested in the convergence of ergodic Markov processes. Such a model is important in many fields including statistic physics, computer science, biology and more. The quantitative analysis of Markov processes is related to several well-known constants such as the spectral gap and the logarithmic Sobolev constant. One aspect of my research is to determine these constants. I also work on one of the most striking probabilistic observation, which is named the cutoff phenomenon, by Diaconis and Shahshahani in early 80's. In a word, Markov chains that presentating a cutoff show a sharp phase transition in their behavior: The distance between the distribution of a chain and its stationarity holds at almost its maximum for a while, then goes down in a relatively short time to a small value and converges to 0 exponentially fast. What surprising is that such a phenomenon happens frequently in real world. My research in this aspect is to find an equivalent condition for a cutff and fix the cutoff time, the time that a cutoff happens.

Publications

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1. 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.
2. 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.
3. 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.
4. Guan-Yu Chen and Laurent Saloff-Coste The cutoff phenomenon for randomized riffle shuffle. Random Structures and Algorithms 32 (2008), no. 3, 346--374.
5. 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.
6. Guan-Yu Chen and Laurent Saloff-Coste, The cutoff phenomenon for ergodic Markov processes. Electronic Journal of Probability, 13 (2008), 26--78.
7. Guan-Yu Chen and Laurent Saloff-Coste, The L2-cutoff for reversible Markov processes. J. Funct. Anal. 258 (2010), 2246-2315.

Last modified date:2009/12/24