Published Journal Articles

• Toshio Nakata
  Probabilistic Proofs of Pascal's Recursion Formulas for Sums of Powers
  Integers: Electronic Journal of Combinatorial Number Theory, Vol. 25, (2025), A49
  (article doi:10.5281/zenodo.15536326 (Colgate University)) Open Access
  

• Toshio Nakata
  Large deviations and fairness for a betting game with a constant ratio of capital
  The Mathematical Gazette, Vol. 108, Number 572, (2024), 237 -- 247.
  (article doi:10.1017/mag.2024.62 (Cambridge UP)) (pdf)
  

• Toshio Nakata and Hosam Mahmoud
  Bernoulli convolution of the depth of nodes in recursive trees with general affinities
  Journal of Stochastic Analysis, Vol. 5: No. 2, Article 4, 1--16, (2024)
  (article doi:10.31390/josa.5.2.04 (The LSU Scholarly Repository)) Open Access
  

• Toshio Nakata
  Large deviations of sums mainly due to just one summand for super-heavy tailed distributions
  Bull. Inst. Math. Acad. Sinica (N.S.) Vol. 18, (2023), No. 4, 437--449.
  (article doi:10.21915/BIMAS.2023403 (Acad. Sinica)) Open Access
  

• S. Kubo, T. Nakata, N. Shiraishi
  The lost boarding pass problem: converse results
  The Mathematical Gazette, Vol. 107, Number 569, (2023), 234 -- 240.
  (article doi:10.1017/mag.2023.54 (Cambridge UP)) (pdf))
  

• Toshio Nakata
  Characterisation of equalisation problems via random walks
  The Mathematical Gazette, Vol. 106, Number 565, (2022), 61 -- 67.
  (article doi:10.1017/mag.2022.10 (Cambridge UP)) (pdf)
  

• Toshio Nakata
  Large deviations for super-heavy tailed random walks
  Stat. Prob. Lett., Vol. 180, 109240, (2022), 1--7.
  (article doi:10.1016/j.spl.2021.109240 (Elsevier))
  

• Toshio Nakata
  105.48 Approximations for the Feller games
  The Mathematical Gazette, Vol. 105, Number 564, (2021), 539 -- 543.
  (article doi:10.1017/mag.2021.130 (Cambridge UP)) (pdf)
  

• Yuka Hoshiyama, Toshio Nakata, Asuka Nomura, Yuki Okochi
  104.39 Buffon's needle on a square lattice
  The Mathematical Gazette, Vol. 104, Number 561, (2020), 543 -- 545.
  (article doi:10.1017/mag.2020.117 (Cambridge UP)) (pdf)
  

• Toshio Nakata
  Limit theorems for super-heavy tailed random variables with truncation: Application to the super-Petersburg game
  Bull. Inst. Math. Acad. Sinica (N.S.) Vol. 15, (2020), No. 2, 123--141.
  (article doi:10.21915/BIMAS.2020202 (Acad. Sinica) ) Open Access
  

• Toshio Nakata
  Coupon collector's problem with unlike probabilities
  J. Classical Anal. Vol. 14, Number 2 (2019), 177--180.
  (article doi:10.7153/jca-2019-14-13 (Ele-math, Publishing House Element d.o.o., Zagreb, Croatia) ) Open Access
  

• Toshio Nakata
  Exact laws of large numbers for independent Pareto random variables
  Bull. Inst. Math. Acad. Sinica (N.S.) Vol. 12, (2017), No. 4, 325--338.
  (article doi: 10.21915/BIMAS.2017403 (Acad. Sinica) ) Open Access
  

• Toshio Nakata
  A note on the asymptotics of the maxima for the St. Petersburg game
  Stat. Prob. Lett., Vol. 129, (2017), 284--287.
  (article doi:10.1016/j.spl.2017.06.010 (Elsevier))
  

• Toshio Nakata
  Weak laws of large numbers for weighted independent random variables with infinite mean
  Stat. Prob. Lett., Vol. 109, (2016), 124--129.
  (article doi:10.1016/j.spl.2015.11.017 (Elsevier))
  
  
• Toshio Nakata
  Limit theorems for nonnegative independent random variables with truncation
  Acta Mathematica Hungarica, Vol. 145 No.1, (2015), 1--16.
  (article doi: 10.1007/s10474-014-0474-5 (Springer))
  
  
• Toshio Nakata
  Limit distributions of generalized St. Petersburg games
  Stat. Prob. Lett., Vol. 96, (2015), 307--314.
  (article doi: 10.1016/j.spl.2014.10.010 (Elsevier))
  
  
• Toshio Nakata
  Another Probabilistic Proof of a Binomial Identity
  Fibonacci Quart. Vol. 52, no. 2, (2014), 139--140,
  (article Fibonacci Association , (pdf) Open Access
  doi: 10.1080/00150517.2014.12427904 (Taylor and Francis)
  
  
• Toshio Nakata
  The number of collisions for the occupancy problem with unequal probabilities
  Advances in Applied Probability, Vol.46, No.1, (2014), 168--185.
  (article doi:10.1239/aap/1396360108 (Cambridge UP)) Open Access
  
  
• Keisuke Matsumoto and Toshio Nakata
  Limit theorems for a generalized Feller game
  Journal of Applied Probability, Vol. 50, No. 1, (2013), 54--63.
  (article doi:10.1239/jap/1363784424 (Cambridge UP)) Open Access
  
  
• Toshio Nakata
  Necklace processes via Polya urns
  Journal of Applied Probability, Vol. 46, No. 1, (2009), 284-295.
  (article doi:10.1239/jap/1238592130 (Cambridge UP)) Open Access
  
  
• E. Ando, T. Nakata, and M. Yamashita
  Approximating the Longest Path Length of a Stochastic DAG by a Normal Distribution in Linear Time
  Journal of Discrete Algorithms, Vol. 7, No. 4, (2009), 420--438,
  (article doi:10.1016/j.jda.2009.01.001 (Elsevier)) Open Access
  
  
• Toshio Nakata
  A Poisson approximation for an occupancy problem with collisions
  Journal of Applied Probability, Vol. 45, No. 2, (2008), 430--439.
  (article doi:10.1239/jap/1214950358 (Cambridge UP)) Open Access
  
  
• Toshio Nakata
  Collision probability for an occupancy problem
  Stat. Prob. Lett. Vol. 78, No. 13, (2008), 1929--1932.
  (article doi:10.1016/j.spl.2008.01.061 (Elsevier))
  
  
• Toshio Nakata
  On the expected time for Herman's probabilistic self-stabilizing algorithm
  Theoretical Computer Science, Vol. 349, No. 3, (2005), 475--483.
  (article doi:10.1016/j.tcs.2005.05.022 (Elsevier)) Open Access
  
  
• Toshio Nakata
  A remark on birth-and-death chains in a random environment
  Bulletin of Fukuoka University of Education III, Vol. 53, (2004), 1--6.
  (article https://libopac.fukuoka-edu.ac.jp/dspace/handle/10780/369 (Fukuoka U. of Educ.)) Open Access
  
  
• T. Nakata, H. Imahayashi and M. Yamashita
  A Probabilistic Local Majority Polling Game on Weighted Directed Graphs
  with an Application to the Distributed Agreement Problem
  Networks, Vol. 35, No. 4, (2000), 266--273.
  (article doi: 10.1002/1097-0037(200007)35:4<266::AID-NET5>3.0.CO;2-4 ( Wiley))
  
  
• Toshio Nakata
  Pianigiani-Yorke measures for non-H\"older continuous potentials
  Hiroshima Mathematical Journal, Vol. 28, No. 1, (1998), 95--111.
  (article doi:10.32917/hmj/1206126873 (Project Euclid)) Open Access
  
  
• Toshio Nakata
  An approximation of Hausdorff dimensions of generalized cookie-cutter Cantor sets
  Hiroshima Mathematical Journal, Vol. 27, No. 3, (1997), 467--475.
  (article doi:10.32917/hmj/1206126964 (Project Euclid)) Open Access
  
  
• Toshio Nakata and Munetaka Nakamura
  On the Julia sets of rational functions of degree two with two real parameters
  Hiroshima Mathematical Journal, Vol. 26, No. 2, (1996), 253--275.
  (article doi:10.32917/hmj/1206127360 (Project Euclid)) Open Access

• Toshio Nakata
  Large deviations of sums mainly due to just one summand for super-heavy tailed distributions
  Bernoulli-ims 11th World Congress in Probability and Statistics,
  August 13, 2024, Ruhr University Bochum
  (conference page) (abstract file) Abstract
  Bochum, Germany
  
  
• Toshio Nakata
  Large deviations for super-heavy tailed random walks
  10th International Workshop on Applied Probability (IWAP2023),
  June 9, 2023, Porto Palace Hotel and Conference Center
  (conference page) (abstract file) Abstract page 117.
  Thessaloniki, Greece
  
  
• Toshio Nakata
  Laws of large numbers for independent Pareto random variables with infinite mean
  12th International Vilnius Conference on Probability Theory and Mathematical Statistics
  and 2018 IMS Annual Meeting on Probability and Statistics,
  July 3, 2018, Vilnius University
  (conference page) (abstract file) Abstract page 272.
  Vilnius, Lithuania
  
  
• Toshio Nakata
  The asymptotics of the maxima for the distribution of the generalized St. Petersburg game
  10th Extreme Value Analysis Conference,
  June 26, 2017, Delft University of Technology (TU Delft)
  (conference page) (abstract file) Abstract page 57.
  Delft, Netherlands
  
  
• Toshio Nakata
  Weak laws of large numbers for weighted independent random variables with infinite mean,
  World Congress in Probability and Statistics,
  July 11, 2016, University of Toronto, the Fields Institute,
  (conference page) (abstract file) Abstract page 82.
  Toronto, Canada
  
  
• Toshio Nakata
  Limit theorems for nonnegative independent random variables with truncation
  International Congress of Mathematicians,
  Aug. 18, 2014, COEX, Convention & Exhibition
  (conference page) (program) Abstract, page 425.
  Seoul, Korea
  
  
• Toshio Nakata
  The number of collisions for the occupancy problem
  8th World Congress in Probability and Statistics,
  July 11, 2012, Grand Cevahir Hotel and Convention Center
  (conference page) page 169,
  Istanbul, Tukey
  
  
• Toshio Nakata
  Integral transforms that preserve Schur convexity with an application to occupancy problem with collisions
  2011 Second International Conference on Networking and Computing,
  Dec 1, 2011, Osaka University Convention Center
  IEEE computer society CS Digital Library
  (article 352--359 (2011). doi:10.1109/ICNC.2011.69, (conference page))
  Osaka, Japan
  
  
• Toshio Nakata
  On the number of collisions for the balls-and-urns problem with unequal probabilities
  7TH INTERNATIONAL CONFERENCE ON LATTICE PATH COMBINATORICS AND APPLICATIONS,
  July 5, 2010, Universita degli Studi di Siena
  (conference page)(Soccer in Siena) 209--212 (2010).
  Siena, Italy
  
  
• Toshio Nakata and Izumi Kubo
  A coupon collector's problem with bonuses
  Fourth Colloquium on Mathematics and Computer Science Algorithms, Trees, Combinatorics and Probabilities
  Sep. 20, 2006, Institut Elie Cartan
  Discrete Mathematics and Theoretical Computer Science, AG, 215--224, (2006),
  (pdf: doi:10.46298/dmtcs.3515 (DMTCS))( abstract )
  Nancy, France
  
  
• E. Ando, M. Yamashita, T. Nakata, Y. Matsunaga,
  The Statistical Longest Path Problem and Its Application to Delay Analysis of Logical Circuits
  ACM/IEEE International Workshop on Timing Issues in the Specification and Synthesis of Digital Systems (TAU'02),
  Dec. 3. 2002, Double Tree Hotel
  (article(ACM)) doi:10.1145/589411.589440, p.134--139 (2002).
  Monterey, USA
  
  
• T. Nakata, and M. Yamashita
  Some Upper Bounds on Expected Agreement Time of a Probabilistic Local Majority Polling Game
  VIII International Colloquium on Structural Information and Communication Complexity
  June 2001, Hotel Vall De Nuria
  Carleton Scientific, 11, 293--304 (2001).
  (pdf) (SIROCCO 2001) (conference page)
  Vall de Nuria, Spain
  
  
• T. Nakata, H. Imahayashi and M. Yamashita
  Probabilistic Local Majority Voting for the Agreement Problem on Finite Graphs
  Computing and Combinatorics: 5th Annual International Conference
  July 26--28, Chuo University, Surugadai
  Lecture Notes in Computer Science 1627, 330--338, (1999).
  (doi:10.1007/3-540-48686-0_33 (Springer)) COCOON 99
  Tokyo, Japan
  
  

• American Math. Monthly, Problem 11356 .
  • Problem: vol. 115 April 2008, p.365.
  • Solution: vol. 117 February 2010, 183--184.
  • My solution: (pdf)
• American Math. Monthly, Problem 11369 .
  • Problem: vol. 115 June-July2008, p.567.
  • Solution: 117 April 2010, p.377.
  • My solution: (pdf)
• The Fibonacci Quarterly H-777 (Lucky Number!) (pdf)
  • Problem: vol. 53 No. 4, 2015, p.372,
    Proposed by Kiyoshi Kawazu, Izumi Kubo and Toshio Nakata.
  • Solution: 55 No. 3, 2017, 285--287.
    Sums of Products of Binomial Coefficients, pdf