Research by T. Zamrik
Welcome. This is where I keep my research: working papers on stochastic analysis, control and mean field games; Jupyter notebooks that work a question through in code, to download or to run on Kaggle; and a blog that takes a question from the world and works it through to the mathematics, with data and models you can run in the browser. The newest of each is just below. — T. Zamrik
36 papers since 2022 · 3 notebooks · 69 blog posts · 6 research areas
Latest
New papers
Queue-Reactive Dynamics on the Full Order-Book Profile
Queue-reactive models of the limit order book make order arrival and cancellation rates functions of the current queue size, and reproduce the mean…
Skew Brownian Motion: One Biased Site and the Asymmetry It Buys
Skew Brownian motion is ordinary Brownian motion everywhere except one point: at the origin each excursion chooses the positive side with probability α…
The Contact Field: Ray-Knight Laws and Reaction in a Distributed Reactive Medium
A particle diffusing through a reactive medium reacts not on first contact but when the contact it has accumulated crosses a threshold, so the quantity…
New notebooks
The Cellar That Is Warmest in Winter
A runnable notebook: Fourier's yearly temperature wave in the ground, solved by Crank–Nicolson, reversed at 7 m, and read back from two thermometers.
The Noise That Looks Like Correlation
A runnable notebook: the Marchenko–Pastur law separates noise from structure in a correlation matrix, and cleaning it fixes a portfolio's promised risk.
The Jensen Gap at Grand Forks, 1997
A runnable notebook: the Weather Service's own outlook record, the 49-foot forecast, the 52-foot dikes and Jensen's gap, computed in Python.
From the Blog
The Shock That Refuses to Break
A weak tidal bore arrives as a train of waves whose first wave is twice the step. The KdV equation, solved, with a live board for any river.
The Rule That Fits One Ward
At 85% occupancy a 100-bed ward is full about once a month, a 20-bed ward within a week, a 500-bed hospital every six years. The OU first-passage maths.
The Barrier That Comes Early
A price at $100 takes nine years on average to reach $120, yet has a 40% chance within a year. The GBM hitting-time formula and up-and-out options.
All 36 papers →All 3 notebooks →All 69 essays →
Research interests
I work on stochastic analysis and optimal control, and on what happens when many decision-makers optimise at once: mean field games, market models and mathematical finance. A typical paper starts from a practical question, when to act and how hard, and ends with an equation solved as explicitly as it allows and checked numerically.
Browse by area
Reading and citing
Most papers, and all of the notebooks and the blog, are free to read; a few papers are restricted. Every paper carries its own serial number, printed on the paper and in its address, so a citation always points at one document (how to cite). Where a paper’s code is published, it is on GitHub, at github.com/Dr-Zamrik, so its numbers can be re-run rather than taken on trust.
Each notebook is a Jupyter notebook you can download as an .ipynb or run on Kaggle, where its numbers are checked against the page before it carries its Kaggle button.
The blog starts from a story and ends in the mathematics, with data, code and live models; some essays grow into papers.
