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Nakashima Lab
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The lab uses probability theory to explore the random behavior of branching processes and polymers.
AboutAbout the lab
Studying random models with probability theory.
Associate Professor Makoto Nakashima studies probability theory, focusing especially on branching processes, a population model in biology.
Probability theory here means measure-theoretic probability, in which probability is defined using measures.
In polymer models, one of the objects of study, a phase transition appears in which the shape changes greatly through interaction with impurities.
The professor is also interested in how the scaling limits of discrete models reveal connections to partial differential equations and stochastic partial differential equations.
Key terms
- Branching process
- A type of probabilistic model for biological populations, often treated as a discrete model.
- Measure-theoretic probability
- Probability theory that defines probability using measures. It can describe mathematically even things like infinitely many trials.
- Phase transition
- A phenomenon in which the shape of a polymer model changes greatly when a parameter, such as the concentration of impurities, is varied.
ResearchResearch themes
The lab investigates the properties of models with random elements from the viewpoint of probability theory. Centered on branching processes, a biological population model, and probabilistic models of polymers, it focuses on new phenomena that emerge from large-scale interactions.
*Illustrative imageBranching processes and scaling limits
The lab studies branching processes, a population model in biology. Considering the scaling limits of discrete models can reveal connections to partial differential equations and stochastic partial differential equations.
*Illustrative imagePolymer models and phase transitions
Polymers in an ideal solvent are studied by regarding them as paths of Brownian motion, the limit of random walks. Interaction with impurities gives rise to a phase transition, and recently the lab has been exploring the universal structure of the model through the behavior of the free energy.
MembersFaculty
- Associate ProfessorMakoto Nakashima
VoicesStudent voices
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Report an errorAbout the images
The top and research theme images are illustrative and were not taken at the lab. They are cropped from Wikimedia Commons images. Cropped CC BY-SA images are provided under the same CC BY-SA license as the original (version shown on each line).
- Top image: “Galton-watson(poisson(1),11gen, 47noeud)” Ipipipourax, S. Roger / CC0 (cropped)
- Branching processes and scaling limits: “Tree of life zoom you are here” Pablo Carlos Budassi / CC BY-SA 4.0 (cropped)
- Polymer models and phase transitions: “Styrene-butadiene chain” Gmrozz / CC BY-SA 4.0 (cropped)
- Related lab (Differential Geometry Lab): “Surfaces of constant positive Gaussian curvature” Salix alba / CC BY-SA 4.0 (cropped)
- Related lab (Probability Theory and Statistical Mechanics Lab): “Polymer solvent mixture” DMDusza / CC0 (cropped)
- Related lab (Fourier Analysis, Partial Differential Equations, and Fluid Dynamics Lab): “Flow separation” Jaganath at English Wikipedia / CC BY-SA 3.0 (cropped)
- Related lab (Topology and Differential Geometry Lab): “Schwarz P Surface” Anders Sandberg / CC BY-SA 3.0 (cropped)
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