Genuinely discrete discrete probability

Key facts

Genuinely discrete discrete probability

What “genuinely discrete” methods can be used with discrete random variables?

When we first learn probability, we start with discrete random variables – experiments whose outcomes take values are non-negative whole numbers. But we then move on to continuous random variables, where we have richer techniques and results – like moments, scaling, shifting, the law of large numbers, the vital importance of the normal distribution, and the central limit theorem.

But what if we instead try to stay in those “early days” of learning probability, and stick firmly to the integers, looking for “genuinely discrete” ideas? We might then look at factorial moments, the probability generating function, “thinning”, the vital importance of the Poisson distribution, and the “law of thin numbers”.

There are plenty of easy-to-state problems regarding “genuinely discrete” discrete probability that have not received the attention they deserve. What is the discrete equivalent of the normal distribution? Which distributions are changed the least by adding independent copies? What symmetries can we observe between high-variance and low-variance distributions? Which discrete random variables are the “most random”?

To apply for this project you will need to make a formal application for research degree study through the University website. You will need to create a login ID with a username and PIN.

• For Application type please select Research Degrees – Research Postgraduate.

• The admission year for this project is 2027/28 Academic Year.

• You will need to select your Planned Course of Study from a drop-down menu. For this project, scroll down and select PHP Statistics Full Time.

• The project start date for this project is 1 October 2027, please use this as your Proposed Start Date of Research.

• Please state clearly in the Research Information Section that the research degree you wish to be considered for is Genuinely discrete discrete probability as well as Dr Matthew Aldridge as your proposed supervisor.

Please state clearly in the Finance section, the funding that you are applying for, if you are self-funding or externally sponsored.

More information on how to apply is available on our website here. You will be required to provide a personal statement which outlines your interest in the project you are applying for, why you have chosen it and how your skills map onto the requirements of the project.

We will assess applications continuously as we receive them. We welcome and strongly encourage any potential applicants to contact the supervisor(s) for an informal discussion, prior to applying, and recommend submitting your application early.

If you are applying with external sponsorship or you are funding your own study, please ensure you provide your supporting documents at the point you submit your application:

Full Transcripts of all degree study or if in final year of study, full transcripts to date including the grading scheme

Personal Statement outlining your interest in the project

If English is not your first language, you must provide evidence that you meet the University's minimum English language requirements (below).

As an international research-intensive university, we welcome students from all walks of life and from across the world. We foster an inclusive environment where all can flourish and prosper, and we are proud of our strong commitment to student education. Across all Faculties we are dedicated to diversifying our community and we welcome the unique contributions that individuals can bring, and particularly encourage applications from, but not limited to Black, Asian, people who belong to a minority ethnic community, people who identify as LGBT+ and people with disabilities. Applicants will always be selected based on merit and ability.

Applicants to research degree programmes should normally have at least a first class or an upper second class British Bachelors Honours degree (or equivalent) in an appropriate discipline. The criteria for entry for some research degrees may be higher, for example, several faculties, also require a Masters degree. Applicants are advised to check with the relevant School prior to making an application. Applicants who are uncertain about the requirements for a particular research degree are advised to contact the School or Graduate School prior to making an application.

The minimum English language entry requirement for research postgraduate research study is an IELTS of 6.0 overall with at least 5.5 in each component (reading, writing, listening and speaking) or equivalent. The test must be dated within two years of the start date of the course in order to be valid. Some schools and faculties have a higher requirement.

This is a non funded PhD project. Applicants are expected to be self funded or to secure external funding.

You can find out more about our Funding Opportunities on our Postgraduate Research Opportunities website.

Important: Please note that all costs associated with your arrival at Leeds (visa, Immigration Health Surcharge, flights etc) would have to be met by yourself, or you will need to find an alternative funding source.

For general enquiries about your application, including how to apply, please contact PGR Admissions by email to phd@engineering.leeds.ac.uk

For questions about this research project, please contact Dr Matthew Aldridge by email to m.aldridge@leeds.ac.uk

• Type of research degree: PhD
• Application deadline: Monday 31 May 2027
• Project start date: Friday 1 October 2027
• Country eligibility: International (open to all nationalities, including the UK)
• Funding: Non-funded
• Supervisors: Dr Matthew Aldridge
• Schools: School of Mathematics
• Research groups/institutes: Probability and Financial Mathematics, Statistics

Research areas