Scaling limits of random growth models

Random growth processes occur widely in the physical world. One of the most well-known, yet notoriously difficult, examples is diffusion-limited aggregation (DLA) which models e.g. mineral deposition. This process is usually initiated from a cluster containing a single "seed" particle, to which successive particles then attach themselves. One approach to mathematically modelling planar random growth seeded from a single particle is to take the seed particle to be the unit disk and to represent the randomly growing clusters as compositions of conformal mappings of the exterior disk. In 1998, Hastings and Levitov proposed a family of models using this approach, which includes a version of DLA. These models appear to exhibit a phase transition from disk-like clusters to random fractal clusters. This project will explore variants of the Hastings-Levitov family with the aim of establishing a mechanism for the breakdown of isotropic behaviour.

<p>Formal applications for research degree study should be made online through the&nbsp;<a href="https://www.leeds.ac.uk/research-applying/doc/applying-research-degrees">University&#39;s website</a>. Please state clearly in the Planned Course of Study section that you are applying for <em><strong>PHD Statistics FT</strong></em>, in the research information section&nbsp;that the research project you wish to be considered for is <em><strong>Scaling limits of random growth models</strong></em>&nbsp;as well as&nbsp;Professor Amanda Turner as your proposed supervisor&nbsp;and in the finance section, please state clearly&nbsp;<em><strong>the funding source that you are applying for, if you are self-funding or externally sponsored</strong></em>.</p> <p>If English is not your first language, you must provide evidence that you meet the University&#39;s minimum English language requirements (below).</p> <p><em>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.</em></p> <p>Please note that you must provide the following documents at the point you submit your application or by the closing date of 3 April 2024 for Leeds Opportunity Research Scholarship or 8 April 2024 for Leeds Doctoral Scholarship:</p> <ul> <li>Full Transcripts of all degree study or if in final year of study, full transcripts to date</li> <li>Personal Statement outlining your interest in the project</li> <li>CV</li> </ul>

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<p><strong>Self-Funded or externally sponsored students are welcome to apply.</strong></p> <p>UK&nbsp;&ndash;&nbsp;The&nbsp;<a href="https://phd.leeds.ac.uk/funding/209-leeds-doctoral-scholarships-2022">Leeds Doctoral Scholarships</a>,&nbsp;<a href="https://phd.leeds.ac.uk/funding/234-leeds-opportunity-research-scholarship-2022">Leeds Opportunity Research Scholarship</a>&nbsp;and <a href="https://phd.leeds.ac.uk/funding/55-school-of-mathematics-scholarship">School of Mathematics Scholarships</a>&nbsp;are available to UK applicants.&nbsp;&nbsp;<a href="https://phd.leeds.ac.uk/funding/60-alumni-bursary">Alumni Bursary</a>&nbsp;is available to graduates of the University of Leeds.</p> <p><strong>Non-UK</strong>&nbsp;&ndash; &nbsp;The&nbsp;<a href="https://phd.leeds.ac.uk/funding/48-china-scholarship-council-university-of-leeds-scholarships-2021">China Scholarship Council - University of Leeds Scholarship</a>&nbsp;is available to nationals of China (now closed for 2024/25 entry). The&nbsp;<a href="https://phd.leeds.ac.uk/funding/73-leeds-marshall-scholarship">Leeds Marshall Scholarship</a>&nbsp;is available to support US citizens.&nbsp;<a href="https://phd.leeds.ac.uk/funding/60-alumni-bursary">Alumni Bursary</a>&nbsp;is available to graduates of the University of Leeds.</p> <p><strong>Important:&nbsp;</strong>&nbsp;Any costs associated with your arrival at the University of Leeds to start your PhD including flights, immigration health surcharge/medical insurance and Visa costs are not covered under this studentship.</p> <p>Please refer to the&nbsp;<a href="https://www.ukcisa.org.uk/">UKCISA</a>&nbsp;website for information regarding Fee Status for Non-UK Nationals.</p>

<p>For general enquiries about applications, contact Doctoral College Admissions by email to&nbsp;<a href="mailto:maps.pgr.admissions@leeds.ac.uk">maps.pgr.admissions@leeds.ac.uk</a></p> <p>For questions about the research project, contact Professor Amanda Turner by email to&nbsp;<a href="mailto:a.turner5@leeds.ac.uk">a.turner5@leeds.ac.uk</a>.<br /> &nbsp;</p>