Probability and Statistics


REF results

Please go to the REF 2014 website to view our results.

Examples of current research

Theoretical Modelling and Empirical Analysis of Wealth and Income Distributions

For details of this project, click here.

For more information on this project and related research areas, contact Enrico Scalas.


Counting and Classifying

For details of this project, click here.

For more information on this project and related research areas, contact Enrico Scalas.

Stochastic Models for Non-stationary Data

For details of this project, click here.

For more information on this project and related research areas, contact Enrico Scalas.

Discrete Hammersley Process

For details of this project, click here.

For more information on this project and related research areas, contact Nicos Georgiou.

Optimal Sequence Alignments 

Probability and statistics webpage

For details of this project, click here.

For more information on this project and related research areas, contact Nicos Georgiou.

Inhomogeneous Last Passage Times

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For details of this project, click here.

For more information on this project and related research areas, contact Nicos Georgiou.

Probability Problems from Gauge Theory
For details of this project, click here.                            

For more information on this project and related research areas, contact Antoine Dahlqvist.  

Geometry of Large Random Trees
For details of this project, click here.                            

For more information on this project and related research areas, contact Minmin Wang.  

Scaling Limits of Critical Random Graphs
For details of this project, click here.                            

For more information on this project and related research areas, contact Minmin Wang.  



Butt, Jacob S, Georgiou, Nicos and Scalas, Enrico (2023) Queuing models with Mittag-Leffler inter-event times. Journal of Fractional Calculus and Applied Analysis. pp. 1-39. ISSN 1311-0454

Cristofaro, Lorenzo, Garra, Roberto, Scalas, Enrico and Spassiani, Ilaria (2023) A fractional approach to study the pure-temporal Epidemic Type Aftershock Sequence (ETAS) process for earthquakes modeling. Fractional Calculus and Applied Analysis, 26. pp. 461-479. ISSN 1311-0454


Harris, Simon C, Horton, Emma, Kyprianou, Andreas E, Wang, Minmin and Unset (2022) Yaglom limit for critical non-local branching Markov processes. Annals of Probability, 50 (6). ISSN 0091-1798

Olivares-Sanchez, Hector Raul, Rodriguez-Martinez, Carlos Manuel, Coronel-Brizio, Hector Francisco, Scalas, Enrico, Seligman, Thomas Henry and Hernandez-Montoya, Alejandro Raul (2022) An empirical data analysis of "price runs" in daily financial indices: dynamically assessing market geometric distributional behavior. PLoS One, 17 (7). e0270492. ISSN 1932-6203

Cox, Alexander M G, Harris, Simon C, Kyprianou, Andreas E and Wang, Minmin (2022) Monte Carlo methods for the neutron transport equation. SIAM-ASA Journal on Uncertainty Quantification, 10 (2). ISSN 2166-2525

Georgiou, Nicos and Scalas, Enrico (2022) Bounds for mixing times for finite semi-Markov processes with heavy-tail jump distribution. Fractional Calculus and Applied Analysis, 25 (1). pp. 229-243. ISSN 1311-0454

Little, Alex, Mezzadri, Francesco and Simm, Nick (2022) On the number of real eigenvalues of a product of truncated orthogonal random matrices. Electronic Journal of Probability, 27. a5 1-32. ISSN 1083-6489


Kadankova, Tetyana, Leonenko, Nikolai and Scalas, Enrico (2021) Fractional non-homogeneous Poisson and Pólya-Aeppli processes of order k and beyond. Communications in Statistics: Theory and Methods. ISSN 0361-0926

Eom, Cheoljun, Kaizoji, Taisei, Livan, Giacomo and Scalas, Enrico (2021) Limitations of portfolio diversification through fat tails of the return distributions: some empirical evidence. North American Journal of Economics and Finance, 56. a101358 1-17. ISSN 1062-9408

Cunden, Fabio Della, Dahlqvist, Antoine and O'Connell, Neil (2021) Integer moments of complex Wishart matrices and Hurwitz numbers. Annales De L'institut Henri Poincaré D. ISSN 2308-5827

Di Nardo, Elvira, Polito, Federico and Scalas, Enrico (2021) A fractional generalization of the Dirichlet distribution and related distributions. Fractional Calculus and Applied Analysis, 24 (1). pp. 112-136. ISSN 1311-0454

Au, Benson, Cébron, Guillaume, Dahlqvist, Antoine, Gabriel, Franck and Male, Camille (2021) Freeness over the diagonal for large random matrices. Annals of Probability, 49 (1). pp. 157-179. ISSN 0091-1798


Dahlqvist, Antoine and Norris, James R (2020) Yang--Mills measure and the master field on the sphere. Communication in Mathematical Physics, 377. pp. 1163-1226. ISSN 1432-0916

Deaño, Alfredo and Simm, Nick (2020) Characteristic polynomials of complex random matrices and Painlevé transcendents. International Mathematics Research Notices. ISSN 1073-7928


Eom, Cheoljun, Kaizoji, Taisei and Scalas, Enrico (2019) Fat tails in financial return distributions revisited: evidence from the Korean stock market. Physica A Statistical Mechanics and its Applications, 526. p. 121055. ISSN 0378-4371

Ciech, Federico and Georgiou, Nicos (2019) Order of the variance in the discrete Hammersley process with boundaries. Journal of Statistical Physics. ISSN 0022-4715

Ponta, Linda, Trinh, Mailan, Raberto, Marco, Scalas, Enrico and Cincotti, Silvano (2019) Modeling non-stationarities in high-frequency financial time series. Physica A: Statistical Mechanics and its Applications, 521. pp. 173-196. ISSN 0378-4371

Bjoernsson, Hjortur, Hafstein, Sigurdur, Giesl, Peter, Scalas, Enrico and Gudmundsson, Skuli (2019) Computation of the stochastic basin of attraction by rigorous construction of a Lyapunov function. Discrete and Continuous Dynamical Systems - Series B, 24 (8). pp. 4247-4269. ISSN 1531-3492

Leonenko, Nikolai, Scalas, Enrico and Trinh, Mailan (2019) Limit theorems for the fractional non-homogeneous Poisson process. Journal of Applied Probability, 56 (1). pp. 246-264. ISSN 0021-9002

Marckert, Jean-François and Wang, Minmin (2019) A new combinatorial representation of the additive coalescent. Random Structures and Algorithms, 54 (2). pp. 340-370. ISSN 1042-9832

Deelan Cunden, Fabio, Mezzadri, Francesco, O'Connell, Neil and Simm, Nick (2019) Moments of random matrices and hypergeometric orthogonal polynomials. Communications in Mathematical Physics. ISSN 0010-3616


Georgiou, Nicos, Khoshnevisan, Davar, Kim, Kunwoo and Ramos, Alex (2018) The dimension of the range of a transient random walk. Electronic Journal of Probability, 23 (83). pp. 1-31. ISSN 1083-6489

Georgiou, Nicos and Ortmann, Janosch (2018) Optimality regions and fluctuations for Bernoulli last passage models. Mathematical Physics, Analysis and Geometry, 21 (22). pp. 1-29. ISSN 1385-0172

Ashton, Stephen, Scalas, Enrico, Georgiou, Nicos and Kiss, István Zoltán (2018) The mathematics of human contact: developing a model for social interaction in school children. Acta Physica Polonica A, 133 (6). pp. 1421-1432. ISSN 0587-4246

Lambert, Gaultier, Ostrovsky, Dmitry and Simm, Nick (2018) Subcritical multiplicative chaos for regularized counting statistics from random matrix theory. Communications in Mathematical Physics, 360 (1). pp. 1-54. ISSN 0010-3616

Eom, Cheoljun, Kaizoji, Taisei, Park, Jong Won and Scalas, Enrico (2018) Realized FX volatility: statistical properties and applications. Future Research Korean Journal of Futures and Options, 26 (1). pp. 1-25. ISSN 1229-988x

Collins, Benoît, Dahlqvist, Antoine and Kemp, Todd (2018) The spectral edge of unitary Brownian motion. Probability Theory and Related Fields, 170 (1-2). pp. 49-93. ISSN 0178-8051

Chen, J M, Hawkes, A G, Scalas, E and Trinh, M (2018) Performance of information criteria for selection of Hawkes process models of financial data. Quantitative Finance, 18 (2). pp. 225-235. ISSN 1469-7688


Scalas, Enrico (2017) Continuous-time statistics and generalized relaxation equations. European Physical Journal B: Condensed Matter and Complex Systems, 90 (11). p. 209. ISSN 1434-6028

During, Bertram, Georgiou, Nicos and Scalas, Enrico (2017) A stylised model for wealth distribution. In: Akura, Yuji and Kirman, Alan (eds.) Economic Foundations of Social Complexity Science. Springer Singapore, Singapore, pp. 95-117. ISBN 9789811057045

Broutin, Nicolas and Wang, Minmin (2017) Reversing the cut tree of the Brownian continuum random tree. Electronic Journal of Probability, 22 (80). pp. 1-23. ISSN 1083-6489

Cébron, Guillaume, Dahlqvist, Antoine and Gabriel, Franck (2017) The generalized master fields. Journal of Geometry and Physics, 119. 34 - 53. ISSN 0393-0440

Bierkens, Joris and Duncan, Andrew (2017) Limit theorems for the zig-zag process. Advances in Applied Probability, 49 (03). pp. 791-825. ISSN 0001-8678

Simm, Nick (2017) On the real spectrum of a product of Gaussian matrices. Electronic Communications in Probability, 22. a41 1-11. ISSN 1083-589X

Deano, Alfredo and Simm, Nicholas (2017) On the probability of positive-definiteness in the gGUE via semi-classical Laguerre polynomials. Journal of Approximation Theory, 220. pp. 44-59. ISSN 0021-9045

Tsourtis, Anastasios, Harmandaris, Vagelis and Tsagkarogiannis, Dimitrios (2017) Parameterization of coarse-grained molecular interactions through potential of mean force calculations and cluster expansion techniques. Entropy, 19 (8). ISSN 1099-4300

Broutin, Nicolas and Wang, Minmin (2017) Cutting down p-trees and inhomogeneous continuum random trees. Bernoulli, 23 (4A). pp. 2380-2433. ISSN 1350-7265

Duquesne, Thomas and Wang, Minmin (2017) Decomposition of Lévy trees along their diameter. Annales de l'Institut Henri Poincaré, Probabilités et Statistiques, 53 (2). pp. 539-593. ISSN 0246-0203

Kasprzak, Mikołaj J, Duncan, Andrew B and Vollmer, Sebastian J (2017) Note on A. Barbour’s paper on Stein’s method for diffusion approximations. Electronic Communications in Probability, 22 (3). pp. 1-8. ISSN 1083-589X

Birmpa, P, Dirr, N and Tsagkarogiannis, D (2017) Large deviations for the macroscopic motion of an interface. Journal of Statistical Physics, 166 (5). pp. 1163-1192. ISSN 0022-4715

Simm, N J (2017) Central limit theorems for the real eigenvalues of large Gaussian random matrices. Random Matrices: Theory and Applications, 6. ISSN 2010-3263


Scalas, Enrico (2016) Random exchange models and the distribution of wealth. European Physical Journal - Special Topics, 225. pp. 3293-3298. ISSN 1951-6355

Baleanu, Dumitru, Diethelm, Kai, Scalas, Enrico and Trujillo, Juan J (2016) Fractional calculus: models and numerical methods (2nd edition). Series on complexity, nonlinearity and chaos, 5 . World Scientific, Singapore. ISBN 9789813140035

Dahlqvist, Antoine (2016) Free Energies and fluctuations for the unitary Brownian motion. Communications in Mathematical Physics, 348 (2). pp. 395-444. ISSN 0010-3616

Deelan Cunden, Fabio, Mezzadri, Francesco, Simm, Nick and Vivo, Pierpaolo (2016) Large-N expansion for the time-delay matrix of ballistic chaotic cavities. Journal of Mathematical Physics, 57 (11901). pp. 1-16. ISSN 0022-2488

Wang, Minmin (2016) Scaling limits for a family of unrooted trees. Latin American Journal of Probability and Mathematical Statistics, 13 (2). pp. 1039-1067. ISSN 1980-0436

Duncan, A B, Kalliadasis, S, Pavliotis, G A and Pradas, M (2016) Noise-induced transitions in rugged energy landscapes. Physical Review E, 94 (3). 032107. ISSN 2470-0045

Duncan, Andrew, Erban, Radek and Zygalakis, Konstantinos (2016) Hybrid framework for the simulation of stochastic chemical kinetics. Journal of Computational Physics, 326. pp. 398-419. ISSN 0021-9991

Georgiou, Nicos, Rassoul-Agha, Firas and Seppäläinen, Timo (2016) Geodesics and the competition interface for the corner growth model. Probability Theory and Related Fields, 169 (1-2). pp. 223-255. ISSN 0178-8051

Fyodorov, Y V and Simm, N J (2016) On the distribution of maximum value of the characteristic polynomial of GUE random matrices. Nonlinearity, 29. pp. 2837-2855. ISSN 0951-7715

Georgiou, Nicos, Rassoul-Agha, Firas and Seppäläinen, Timo (2016) Stationary cocycles and Busemann functions for the corner growth model. Probability Theory and Related Fields, 169 (1-2). pp. 177-222. ISSN 0178-8051

Jansen, Sabine (2016) Continuum percolation for Gibbsian point processes with attractive interactions. Electronic Journal of Probability, 21. p. 47. ISSN 1083-6489

Den Hollander, F and Jansen, S (2016) Berman-Konsowa principle for reversible Markov jump processes. Markov Processes and Related Fields, 22 (3). pp. 409-422. ISSN 1024-2953

Fyodorov, Y V, Khoruzhenko, B A and Simm, N J (2016) Fractional Brownian motion with Hurst index H=0 and the Gaussian Unitary Ensemble. Annals of Probability, 44 (4). pp. 2980-3031. ISSN 0091-1798

Wang, Minmin (2016) Height and diameter of Brownian tree. Electronic Communications in Probability, 20 (88). pp. 1-15. ISSN 1083-589X

Cunden, Fabio Deelan, Mezzadri, Francesco, Simm, Nick and Vivo, Pierpaolo (2016) Correlators for the Wigner–Smith time-delay matrix of chaotic cavities. Journal of Physics A: Mathematical and Theoretical, 49 (18). ISSN 1751-8113

Duncan, A B, Lelièvre, T and Pavliotis, G A (2016) Variance reduction Using nonreversible Langevin samplers. Journal of Statistical Physics, 163 (3). pp. 457-491. ISSN 0022-4715


Duncan, Andrew B (2015) Homogenization of lateral diffusion on a random surface. Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal, 13 (4). pp. 1478-1506. ISSN 1540-3459

Jansen, S (2015) Cluster and virial expansions for the multi-species tonks gas. Journal of Statistical Physics, 161 (5). pp. 1299-1323. ISSN 0022-4715

Duncan, Andrew, Liao, Shuohao, Vejchodský, Tomáš, Erban, Radek and Grima, Ramon (2015) Noise-induced multistability in chemical systems: discrete versus continuum modeling. Physical Review E, 91 (4). 042111. ISSN 1539-3755

Jansen, Sabine, König, Wolfgang and Metzger, Bernd (2015) Large deviations for cluster size distributions in a continuous classical many-body system. Annals of Applied Probability, 25 (2). pp. 930-973. ISSN 1050-5164

Mehta, Dhagash, Hauenstein, Jonathan D, Niemerg, Matthew, Simm, Nicholas J and Stariolo, Daniel A (2015) Energy landscape of the finite-size mean-field 2-spin spherical model and topology trivialization. Physical Review E (PRE), 91. ISSN 1539-3755

Duncan, A M, Elliott, C M, Pavliotis, G A and Stuart, A M (2015) A multiscale analysis of diffusions on rapidly varying surfaces. Journal of Nonlinear Science, 25 (2). pp. 389-449. ISSN 0938-8974


Ercolani, Nicholas, Jansen, Sabine and Ueltschi, Daniel (2014) Random partitions in statistical mechanics. Electronic Journal of Probability, 19. p. 82. ISSN 1083-6489

Jansen, Sabine and Kurt, Noemi (2014) On the notion(s) of duality for Markov processes. Probability Surveys, 11. pp. 59-120. ISSN 1549-5787

Jansen, S and Jung, P (2014) Wigner crystallization in the quantum 1D jellium at all densities. Communications in Mathematical Physics, 331 (3). pp. 1133-1154. ISSN 0010-3616

Jansen, Sabine, Tate, Stephen J, Tsagkarogiannis, Dimitrios and Ueltschi, Daniel (2014) Multispecies virial expansions. Communications in Mathematical Physics, 330 (2). pp. 801-817. ISSN 0010-3616


Mezzadri, F and Simm, N J (2013) Tau-function theory of chaotic quantum transport with β = 1, 2, 4. Communications in Mathematical Physics, 324 (2). pp. 465-513. ISSN 0010-3616


Ponta, Linda, Scalas, Enrico, Raberto, Marco and Cincotti, Silvano (2012) Statistical analysis and agent-based microstructure modeling of high-frequency financial trading. IEEE Journal of Selected Topics in Signal Processing, 6 (4). pp. 381-387. ISSN 1932-4553

Livan, Giacomo, Inoue, Jun-ichi and Scalas, Enrico (2012) On the non-stationarity of financial time series: impact on optimal portfolio selection. Journal of Statistical Mechanics: Theory and Experiment, 2012. P07025. ISSN 1742-5468

Scalas, Enrico and Viles, Noèlia (2012) On the convergence of quadratic variation for compound fractional Poisson processes. Fractional Calculus and Applied Analysis, 15 (2). pp. 314-331. ISSN 1311-0454

Mezzadri, F and Simm, N (2012) Moments of the transmission eigenvalues, proper delay times and random matrix theory II. Journal of Mathematical Physics, 53 (5). 053504-1-053504-42. ISSN 0022-2488


Brydges, David C, Dahlqvist, Antoine and Slade, Gordon (2011) The strong interaction limit of continuous-time weakly self-avoiding walk. Workshop on Probabilistic Techniques in Statistical Mechanics Celebrating the 65th Birthday of Erwin Bolthausen, Berlin, Germany, October 14–16, 2010. Published in: Deuschel, Jean-Dominique, Gentz, Barbara, König, Wolfgang, von Renesse, Max, Scheutzow, Michael and Schmock, Uwe, (eds.) Probability in Complex Physical Systems. 11 275-287. Springer Berlin Heidelberg, Berlin. ISSN 2190-5614 ISBN 9783642238109