### Numerical code

For numerical results appearing in my published work, I try to make the code available here. I generally use MATLAB and R. There's the standard "There could be life-threatening errors in the code." declaration. If you do find an error, I would appreciate an email.

#### k-coverage probability in a single-tier cellular networks:

I wrote some MATLAB and R code to calculate k-coverage probability of a cellular network in the downlink channel. This code is based on a model developed for an ISIT paper, which we later extended to the multi-tier case in this paper with more detailed calculations; see below. The R and the Matlab code should do effectivly the same things. For very small SINR threshold values (less than -12 dB), the respective numerical integration methods will break down. The integration method in R generally performs better than the Matlab one in this sitatution.
My k-coverage probability code has also been used to study a geographic caching strategy in cellular networks, but this is not my work.

#### k-coverage probability in a multi-tier cellular network:

This MATLAB code extends the method of the single-tier setting to that of a multi-tier model for so-called heterogeneous networks. It is based on network models and methods outlined in this paper, which was published in IEEE TOIT. The main idea uses the factorial moment measures of the SINR point process under a Poisson network model.

#### Equivalent Poisson networks:

This Matlab code compares a two-tier network and a single-tier network by plotting the densities of their "equivalent networks". This code is based on a short paper, which demonstrated that different Poisson networks can be considered equivalent or different Poisson networks can be compared with their "equivalent forms".

### Selected talks

Signal-to-interference ratio in wireless communication networks, PDF, Dynamical networks and network dynamics, Edinburgh, 2016.
When do wireless network signals appear Poisson?, PDF, 18th Workshop on Stochastic Geometry, Stereology and Image Analysis, Lingen, 2015.
Large-deviation theory and coverage in mobile phone networks, PDF, University of Melbourne, 2015.
And a mathematical talk without mathematics:
A random walk through the history of random terms, PDF, Weierstrass Institute, 2015.

### Technical Reports

I write technical reports (or hobby articles) on topics that are mostly familiar to me in mathematics. The focus of these reports is on explaining mathematical ideas in everyday language, while giving a detailed historical context. Some of the articles have served as the foundation in corresponding Wikpedia articles.

If there are errors, except for minor typos, in the technical reports, please email me. When writing these articles I am often also learning new material, so it's very possible I've misunderstood concepts and made blunders along the way.

Paul Keeler, "Notes on the Poisson point process". (PDF)
Paul Keeler, "Notes on stochastic processes". (PDF)