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足立
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- URL for Zoom registration
https://zoom.us/meeting/register/tJElceutrj0sGtcHtYV7XlOBPRKbsmmK68xF
- Lecturer
Prof. Kiyoshi Kanazawa (Graduate School of Science, Kyoto University)
- Schedule for lectures
(Tue., Feb. 4) 13:00-14:30, 14:45-16:15, 16:30-18:00
(Wed., Feb. 5) 10:30-12:00, 13:00-14:30, 14:45-16:15
- Schedule for seminar
(Wed., Feb. 5) 16:30-18:00
- Abstract for lectures
Title: Introduction to the stochastic process and its application in physics
Abstract: The stochastic process is a popular tool for broad
disciplines, such as physics, biophysics, chemistry, neuroscience,
economics, and finance. In this lecture course, I will provide an
elementary introduction to stochastic processes in physics without
assuming rigorous background knowledge of probability theories. Most of
the basic topics in stochastic processes will be covered in this lecture
course, such as (1) the one-to-one correspondence between stochastic
differential equations and master equations, (2) their standard forms,
(3) Ito's lemma, and (4) the perturbation theories (the system-size
expansion). I will also present its application to statistical physics,
such as (5) kinetic theory and (6) a microscopic derivation of the
Langevin equation from hard-sphere Hamiltonian dynamics in the dilute
gas limit. My goal is to help the audience calculate most of the main
calculations by their own hands by providing detailed explanations
without abbreviations. This lecture is based on my Japanese notebook,
available on my webpage (URL: https://kanazawa.scphys.kyoto-u.ac.jp/資料/).
- Abstract for seminar
Title: Master equations for general non-Markovian processes: the Hawkes
process and beyond
Abstract: The Markovian process is one of the most important classes of
stochastic processes. The Markovian process is defined as a stochastic
process whose time evolution is independent of the system's entire
history and has been extensively studied using the master equation and
Fokker-Planck equation approaches. In contrast, non-Markovian processes
-- where time evolution depends on the full history of the system --
have not been systematically explored, except for a few special cases,
such as semi-Markovian processes. In this talk, we present a recent
master-equation approach to general non-Markovian jump processes [1-4].
Beginning with a general non-Markovian jump process, we derive the
corresponding master equation through a Markovian-embedding approach.
The Markovian embedding is a scheme to add a sufficient number of
auxiliary variables to convert a non-Markovian model to a
high-dimensional Markovian model. For the case of our model, the
one-dimensional non-Markovian model is shown to be equivalent to a
Markovian stochastic field theory, and we derive the field master
equation correspondingly [4]. As an application, we examine the
nonlinear Hawkes process, a history-dependent and self-exciting model
frequently used in studying complex systems [1-3]. Additionally, we
explore the stochastic thermodynamic framework for general jump
processes [5] as another example.
[1] K. Kanazawa and D. Sornette, Phys. Rev. Lett. 125, 138301 (2020).
[2] K. Kanazawa and D. Sornette, Phys. Rev. Lett. 127, 188301 (2021).
[3] K. Kanazawa and D. Sornette, Phys. Rev. Res. 5, 013067 (2023).
[4] K. Kanazawa and D. Sornette, Phys. Rev. Res. 6, 023270 (2024).
[5] K. Kanazawa and A. Dechant, in preparation.