Michail Loulakis

Thermodynamic limit for the invariant measures in supercritical zero range processes

We prove a strong form of the equivalence of ensembles for the invariant measures of zero range processes conditioned to a supercritical density of particles. It is known that in this case there is a single site that accomodates a macroscopically large number of the particles in the system. We show that in the thermodynamic limit the rest of the sites have joint distribution equal to the grand canonical measure at the critical density. This improves the result of Großkinsky, Schütz and Spohn, where convergence is obtained for the finite dimensional marginals. We obtain as corollaries limit theorems for the order statistics of the components and for the fluctuations of the bulk.

Conditional distribution of heavy tailed random variables on large deviations of their sum

It is known that large deviations of sums of subexponential random variables are most likely realised by deviations of a single random variable. In this article we give a detailed picture of how subexponential random variables are distributed when a large deviation of the sum is observed.

Zero-range condensation at criticality

Zero-range processes with jump rates that decrease with the number of particles per site can exhibit a condensation transition, where a positive fraction of all particles condenses on a single site when the total density exceeds a critical value. We consider rates which decay as a power law or a stretched exponential to a non-zero limiting value, and study the onset of condensation at the critical density. We establish a law of large numbers for the excess mass fraction in the maximum, as well as distributional limits for the fluctuations of the maximum and the fluctuations in the bulk.

Metastability in a condensing zero-range process in the thermodynamic limit

Zero-range processes with decreasing jump rates are known to exhibit condensation, where a finite fraction of all particles concentrates on a single lattice site when the total density exceeds a critical value. We study such a process on a one-dimensional lattice with periodic boundary conditions in the thermodynamic limit with fixed, super-critical particle density. We show that the process exhibits metastability with respect to the condensate location, i.e. the suitably accelerated process of the rescaled location converges to a limiting Markov process on the unit torus. This process has stationary, independent increments and the rates are characterized by the scaling limit of capacities of a single random walker on the lattice. Our result extends previous work for fixed lattices and diverging density [In: Beltran and Landim, Probab Theory Relat Fields 152(3–4):781–807, 2012], and we follow the martingale approach developed there and in subsequent publications. Besides additional technical difficulties in estimating error bounds for transition rates, the thermodynamic limit requires new estimates for equilibration towards a suitably defined distribution in metastable wells, corresponding to a typical set of configurations with a particular condensate location. The total exit rates from individual wells turn out to diverge in the limit, which requires an intermediate regularization step using the symmetries of the process and the regularity of the limit generator. Another important novel contribution is a coupling construction to provide a uniform bound on the exit rates from metastable wells, which is of a general nature and can be adapted to other models.

Spin-noise correlations and spin-noise exchange driven by low-field spin-exchange collisions

The physics of spin exchange collisions have fueled several discoveries in fundamental physics and numerous applications in medical imaging and nuclear magnetic resonance. We here report on the experimental observation and theoretical justification of spin-noise exchange, the transfer of spin-noise from one atomic species to another. The signature of spin-noise exchange is an increase of the total spin-noise power at low magnetic fields, on the order of 1 mG, where the two-species spin-noise resonances overlap. The underlying physical mechanism is the two-species spin-noise correlation induced by spin-exchange collisions.

Exact speed and transmission cost in a simple one-dimensional wireless delay-tolerant network

We study a simple one-dimensional, discrete-time network model that consists of two nodes moving on a discrete circle, changing their direction of movement randomly, and a single packet travelling in the clockwise direction, using combinations of transmissions between the two nodes (when they are co-located) and physical transports on their buffers. In this setting, we provide exact, explicit expressions for the long-term averages of the packet speed and the wireless transmission cost. Our work is a first step towards providing simple and exact results for more realistic wireless delay-tolerant network models.

Quantum Biometrics with Retinal Photon Counting

It is known that the eyes scotopic photodetectors, rhodopsin molecules and their associated phototransduction mechanism leading to light perception, are efficient single photon counters. We here use the photon counting principles of human rod vision to propose a secure quantum biometric identification based on the quantum-statistical properties of retinal photon detection. The photon path along the human eye until its detection by rod cells is modeled as a filter having a specific transmission coefficient. Precisely determining its value from the photodetection statistics registered by the conscious observer is a quantum parameter estimation problem that leads to a quantum secure identification method. The probabilities for false positive and false negative identification of this biometric technique can readily approach

On the symmetry of the diffusion coefficient in asymmetric simple exclusion

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Einstein Relation for a Tagged Particle in Simple Exclusion Processes

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Mobility and Einstein Relation for a tagged particle in asymmetric mean zero random walk with simple exclusion

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