Homepage of Elnur Emrah

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I am currently a senior research associate at the Institute of Probability, Dynamics and Analysis, a research unit within the School of Mathematics at University of Bristol. This is a postdoctoral position supervised by Márton Balázs and funded by his EPSRC grant EP/W032112/1 titled "Particle systems, growth models and their probabilistic structures". I began working in this role in April, 2023.

I am also a co-organizer of the Bristol Probability Seminar, previously with Jessica Jay and now with Erin Russell and Luke Turvey.

Research interests

I work in the field of probability theory with interests in stochastic growth, percolation and polymer models, interacting particle systems, and random matrices.

Past employment

Between January 1, 2019 and December 31, 2022, I worked as a postdoctoral researcher within the Random Matrices, Stochastic Models and Analysis group at KTH under the supervision of Kurt Johansson. During this time, I was involved in the organization of the Random Matrix Theory Seminar at KTH along initially with Diane Holcomb , and then with Maurice Duits and Kevin Schnelli.

I moved to Stockholm from Pittsburgh, PA in January, 2019. Previously, I held a postdoctoral position at Carnegie Mellon University with Steven Shreve as my mentor. Before that, I completed my graduate studies at the University of Wisconsin-Madison in August, 2016. My PhD advisor was Timo Seppäläinen.

Publications

Coupling derivation of optimal-order central moment bounds in exponential last-passage percolation (joint with Nicos Georgiou and Janosch Ortmann). J. Stat. Phys. 192, 24 (2025).

Optimal-order exit point bounds in exponential last-passage percolation via the coupling technique (joint with Chris Janjigian and Timo Seppäläinen). Prob. Math. Phys. 4 (2023) 609-666

Flats, spikes and crevices: the evolving shape of the inhomogeneous corner growth model (joint with Chris Janjigian and Timo Seppäläinen). Electron. J. Probab. 26, 1-45, (2021)

Large deviations for some corner growth models with inhomogeneity (joint with Chris Janjigian). Markov Processes Relat. Fields 23, 267-312 (2017)

Limit shapes for inhomogeneous corner growth models with exponential and geometric weights. Electron. Commun. Probab. Volume 21 (2016), paper no. 42, 16 pp

Preprints

Permutation invariance in last-passage percolation and the distribution of the Busemann process (joint with Erik Bates, James Martin, Timo Seppäläinen and Evan Sorensen). (2025)

Anomalous geodesics in the inhomogeneous corner growth model (joint with Chris Janjigian and Timo Seppäläinen). (2024)

Some slides from 2019 on the above work are available here. (Note the correction on p. 15).

Right-tail moderate deviations in the exponential last-passage percolation (joint with Chris Janjigian and Timo Seppäläinen). (2020)

Thesis

Limit shape and fluctuations for exactly solvable inhomogeneous corner growth models. (2016)

Expository

Fluctuations of the corner growth model with geometric weights. (2016)

Teaching

I taught several undergraduate level classes at CMU including differential equations, discrete-time finance, probability and real analysis.

Undergraduate advising

In 2018, I advised CMU undergraduate students Bryan Ding and Zilin Wang on their summer research project titled Constructing Local Volatility Surfaces to Price Options.

Profile

Google scholar

Math genealogy