福岡大学確率論セミナー

場所：福岡大学理学部9号館4階大学院講義室3
世話人：桑江一洋(福岡大学理学部)，天羽隆史(福岡大学理学部)，江崎翔太(福岡大学理学部)

2019年度のセミナー記録

• 2019年11月21日(木) 16:30-18:00
  • 場所：福岡大学理学部9号館4階大学院講義室3
  • 講師：種村 秀紀 氏（慶應義塾大学理工学部）
  • 題目：Preferential attachment model. Joint work with Rahul Roy (Indian Statistical Institute )
  • 講演要旨：Ben-Ari and Schinazi (2016) introduced a stochastic model to study `virus-like evolving population with high mutation rate'. This model is a birth and death model with an individual at birth being either a mutant with a random fitness parameter in [0,1] or having one of the existing fitness parameters with uniform probability; whereas a death event removes the entire population of the least fit site. We change this to incorporate the notion of `survival of the fittest', by requiring that a non-mutant individual, at birth, has a fitness according to a preferential attachment mechanism, i.e., it has a fitness \(f\) with a probability proportional to the size of the population of fitness \(f\). Also death just removes one individual at the least fit site. This preferential attachment rule leads to a power law behaviour in the asymptotics, unlike the exponential behaviour obtained by Ben-Ari and Schinazi (2016).
• Panki Kim氏講義
  Panki Kim氏の福岡大学滞在に際して, 12月25日(水)夕方に下記の通りの大学院生向けの講演を行いました。
  • 場所: 福岡大学理学部9号館4階大学院講義室4
  • 講師: Panki Kim 氏（Seoul National University）
  • 題目: Levy process and stable process
  • 時間割: 12月25日(水)
    • 14:40--16:10, Levy process and stable process I
    • 16:20--17:50, Levy process and stable process II
• 2019年12月26日(木) 16:30-18:00
  • 場所：福岡大学理学部9号館4階大学院講義室3
  • 講師：盛田 健彦 氏（大阪大学大学院理学研究科）
  • 題目：Central limit theorem for random dynamical systems and their direct products
  • 講演要旨：Given a stationary sequence of random variables taking values in an appropriate family of transformations, let us consider a random dynamical system defined by the composition of elements in the stationary sequence one after another. In this talk I introduce notion of ‘direct product’ of such a random dynamical system and I would like to explain about the relation between the sample-wise (quenched) CLT for random dynamical systems and the sample-averaged (annealed) CLT for their direct products.
• 2020年1月15日(水) 16:30-18:00
  • 場所：福岡大学理学部9号館4階大学院講義室3
  • 講師：Panki Kim 氏（Seoul National University）
  • 題目：Heat kernel estimates and their stabilities for symmetric jump processes with general mixed polynomial growths on metric measure spaces
  • 講演要旨：In this talk, we discuss a symmetric pure jump Markov process X on a general metric measure space that satisfies volume doubling conditions. We study estimates of the transition density p(t,x,y) of X and their stabilities when the jumping kernel for X has general mixed polynomial growths. In our setting, the rate function which gives growth of jumps of X may not be comparable to the scale function which provides the borderline for p(t,x,y) to have either near-diagonal estimates or off-diagonal estimates. Under the assumption that the lower scaling index of scale function is strictly bigger than 1, we establish stabilities of heat kernel estimates. If underlying metric measure space admits a conservative diffusion process which has a transition density satisfying a general sub-Gaussian bounds, we obtain heat kernel estimates. In this case, scale function is explicitly given by the rate function and a function related to walk dimension of underlying space. As an application, we prove that the finite moment condition in terms of F on such symmetric Markov process is equivalent to a generalized version of Khintchine-type law of iterated logarithm at the infinity. This is joint works with Joohak Bae, Jaehoon Kang and Jaehun Lee.
• 2020年3月23日(月) 16:30-18:00
  • 場所：福岡大学理学部9号館4階大学院講義室3
  • 講師：新井 裕太 氏（千葉大学大学院　融合理工学府）
  • 題目：The KPZ fixed point for discrete time TASEPs
  • 講演要旨：The totally asymmetric simple exclusion process (TASEP) is one of the simplest interacting stochastic particle system and can be interpreted as a stochastic growth model of an interface, which turns out to belong to the Kardar-Parisi-Zhang (KPZ) universality class. In this talk we consider two ver- sions of TASEPs with geometric and Bernoulli hopping probabilities. In these processes, we obtain a single Fredholm determinant representation for the joint distribution function of particle positions with arbitrary initial data. Using this, we show that in the KPZ 1:2:3 scaling limit, the distribution function converges to the one describing the KPZ fixed point was introduced by Mateski, Quastel and Remenik. This talk is based on a recent preprint, arXiv:2002.06824.