2.2 高分子のトポロジー的絡み合い効果I: ランダム結び目とランダム絡み目
Topological entanglement of polymers I:
Random knotting and linking (9POP)

原著論文　Original papers

1. T. Deguchi and K. Tsurusaki,
   A Statistical Study of Random Knotting Using the Vassiliev Invariants,
   Journal of Knot Theory and Its Ramifications 3 (1994) 321-353.

2. K. Tsurusaki and T. Deguchi,
   Fractions of Particular knots in Gaussian Random Polygons,
   J. Phys. Soc. Jpn. 64 (1995) 1506-1518.

3. T. Deguchi and K. Tsurusaki,
   Universality of Random Knotting,
   Phys. Rev. E. 55 (1997) 6245-6248.

4. T. Deguchi and K. Tsurusaki,
   Numerical application of knot invariants and universality of random knotting,
   Banacha Center Publications, 42 (1998) 77-85.

5. T. Deguchi and K. Tsurusaki,
   Random knots and links and applications to polymer physics,
   in Lectures at Knots '96, edited by S. Suzuki, (World Scientific, Singapore, 1997) pp. 95-122.

6. M. K. Shimamura, and T. Deguchi,
   Characteristic length of random knotting for cylindrical self-avoiding polygons,
   Phys. Lett. A 274 (2000) pp. 184-191. (cond-mat/0008268)

7. M. K. Shimamura, and T. Deguchi,
   Topological entropy of a stiff ring polymer and its connection to DNA knots, J. Phys. Soc. Jpn. 70 (2001) pp. 1523-1536.

8. A. Yao, H. Matsuda, H. Tsukahara, M. K. Shimamura, and T. Deguchi,
   On the dominance of trvial knots among SAPs on a cubic lattice,
   J. Phys. A: Math. Gen. 34 (2001) pp. 7563-7577 . (cond-mat/0103365)

9. M. K. Shimamura and T. Deguchi,
   Knot complexity and the probability of random knotting,
   Phys. Rev. E 66, R040801 (2002). (cond-mat/0207282)

国際会議の報告　 Proceedings papers of international conferences

1. K. Tsurusaki, T. Deguchi and M. Wadati,
   A Topological Study of Random Walks, Field Theory and Collective Phenomena, the Proceedings of the Workshop at Perugia on May 1992, ed. by S. De Lillo, F.C. Khanna, G.W. Semenoff, P. Sodano (World Sci. Co., Singapore 1995) pp. 185-206.

2. K. Tsurusaki and T. Deguchi
   Numerical analysis on Topological Entanglements of random polygons,
   Statistical Models, Yang-Baxter Equation and Related Topics, eds. M.L. Ge and F.Y. Wu, the proceedings of the Satellite Meeting of STATPHYS-19, Nankai Institute, Tianjin, China, 8-10 August 1995, (World Scientific, Singapore, 1996) pp. 320-329.

3. T. Deguchi and K. Tsurusaki,
   On a universality of random knotting,
   Bussei-Kenkyu 66 (1996) pp. 434-435.

4. K. Tsurusaki and T. Deguchi ,
   The linking probability of ring polymers with excluded volume,
   the Proceedings of the 2nd Tohwa University International Meeting Statistical Physics, Fukuoka, Japan, ed. by M. Tokuyama and I. Oppenheimer (World Sci., 1998) p. 199.

国内研究会の報告　 Reports of workshops in Japan

1. 出口　哲生、
   「高分子のトポロジー的絡み合いと結び目理論」（招待講演）、
   ゲルワークショップ イン　河口湖 （２００２年８月５日ー７日） 高分子学会主催、講演要旨集(2002) pp. 5-8.

解説（日本語）

1. 出口 哲生、
   結び目とDNA、
   パリテイ Vol. 11 (1996) No. 8, pp. 39-42.

2. 出口 哲生、
   ランダム結び目と高分子の物理学、
   数理科学１９９７年１２月号 pp. 12-19.