All talks will be held in Room MI1, Mathematical Institute, University of Warwick. The conference starts at 14:00 and finishes at 19:00. We are planning to take speakers out for dinner after the conference.
A brief introduction is given to the `second-quantised' description of the master equation for diffusion-limited reactions, and its connection to Langevin equations with (complex) noise. The method is applied to the reversible reaction
Persistence has, in short time, become a widely studied topic in nonequilibrium statistical mechanics. I will review persistence in the context of phase separation dynamics (from which it emerged) and focus attention on some understudied aspects: persistence in conserved order parameter systems and the universality classes of persistence. In particular, I will describe what Lifshitz-Slyozov theory and its variants can teach us about these topics.
Consider a non-equilibrium state of non-interacting Fermi gas obtained by application of an arbitrary time-dependent potential to the Fermi gas in the ground state. We develop a general method that yields quantum statistics of any single-particle operator (charge, energy, momentum, etc...) in this non-equilibrium state. The quantum statistics is expressed analytically through a solution of an auxiliary matrix Riemann-Hilbert problem.
A discrete version of Pitman's theorem states that, if X is a simple random walk with positive drift, and M(n) is its maximum up to time n, then the process 2M-X is Markov and has the same law as that of X conditioned to stay positive. I will show how the classical output theorem for the stable, stationary M/M/1 queue, namely that the output has the same law as the input, can be used to prove this and, moreover, to obtain a multi-dimensional generalisation. This carries over to the Brownian motion setting, and in this context there is a direct connection with eigenvalues of random matrices. (This joint work with Marc Yor.) I will then explain briefly how all this is related to the Schensted correspondence between "words" and pairs of "tableaux". Making this connection yields an alternative proof of the above representation theorem and reveals more of the mathematical structure of the processes involved. It also highlights the connections with two growth models: the "corner growth model" (studied by Johansson) and the growth model obtained by watching the evolution of the shape of the tableaux obtained by applying Schensted's algorithm to a random word.
Nonequilibrium phase transitions in a system of diffusing, coagulating, fragmenting particles interacting with the environment through adsorption and desorption of particles will be discussed. The different phases as well as the critical exponents describing the transitions will be characterized.
We present a new theoretical framework for Diffusion Limited Aggregation and associated Dielectric Breakdown Models in two dimensions. Key steps are understanding how these models interrelate when the ultra-violet cut-off strategy is changed, the analogy with turbulence and the use of logarithmic field variables. Within the simplest, Gaussian, truncation of mode-mode coupling, all properties can be calculated. The agreement with prior knowledge from simulations is encouraging, and a new superuniversality of the tip scaling exponent is both predicted and confirmed.