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Whereas nonrelativistic mechanics always connects the total momentum of a system to the motion of the center of mass, relativistic systems, such as interacting electromagnetic charges, can have internal linear momentum in the absence of…
For a one-dimensional random walk in random scenery (RWRS) on Z, we determine its quenched weak limits by applying Strassen's functional law of the iterated logarithm. As a consequence, conditioned on the random scenery, the one-dimensional…
Under reasonable algebraic assumptions and under an infinite second order moment assumption, we show that the logarithm of the norm (log-norm) of a product of random i.i.d. matrices with entries in $\mathbb{R}$ or in any other local field…
It is a well-known conjecture in $\beta$-models and in their discrete counterpart that, generically, external potentials should be ``off-critical'' (or, equivalently, ``regular''). Exploiting the connection between minimizing measures and…
We consider a class of particle systems which appear in various applications such as approximation theory, plasticity, potential theory and space-filling designs. The positions of the particles on the real line are described as a global…
We consider certain two-dimensional systems with self--dual points including uniform and disordered $q$-state Potts models. For systems with continuous energy density (such as the disordered versions) it is established that the self--dual…
We consider directed random polymers in $(d+1)$ dimensions with nearly gamma i.i.d. disorder. We study the partition function $Z_{N,\omega}$ and establish exponential concentration of $\log Z_{N,\omega}$ about its mean on the subgaussian…
The binding of clusters of metal nanoparticles is partly electrostatic. We address difficulties in calculating the electrostatic energy when high charging energies limit the total charge to a single quantum, entailing unequal potentials on…
We show that the correlations of electrons with a fixed energy in metals have very anomalous time and space dependences. Due to soft modes that exist in any Fermi liquid, combined with the incomplete screening of the Coulomb interaction at…
The existence of quasi-long range order is demonstrated in nonequilibrium steady states in isotropic $XY$ spin chains including of two types of additional terms that each generate a gap in the energy spectrum. The system is driven out of…
In order to understand the nature of friction in closely-packed granular materials, a discrete element simulation on granular layers subjected to isobaric plain shear is performed. It is found that the friction coefficient increases as the…
The asymptotic behaviour of the electromagnetic form factors of the electron and quark is obtained in the double-logarithmic approximation for Sudakov kinematics, i.e. for the case that the value of the momentum transfer is much greater…
Frontal polymerization is a promising energy-saving method for rapid fabrication of polymer components with good mechanical properties. In these systems, a small energy input is sufficient to convert monomers, from a liquid or soft solid…
This dissertation develops, for several families of statistical mechanical and random growth models, techniques for analyzing infinite-volume asymptotics. In the statistical mechanical setting, we focus on the low-temperature phases of spin…
Limit theorems for non-additive probabilities or non-linear expectations are challenging issues which have raised progressive interest recently. The purpose of this paper is to study the strong law of large numbers and the law of the…
We study loop corrections to positivity bounds on effective field theories in the context of $2\to 2$ scattering in gravitational theories, in the presence of light particles. It has been observed that certain negative contributions at low…
For open systems subjected to external magnetic fields, relations between the statistical cumulants of their fluctuating currents and their response coefficients are established at arbitrary orders in the deviations from equilibrium, as a…
We explore a possible connection between two aspects of Loop Quantum Gravity which have been extensively studied in the recent literature: the black-hole area-entropy law and the energy-momentum dispersion relation. We observe that the…
We discuss the theoretical treatment of non-global observables, those quantities that are sensitive only to radiation in a restricted region of phase space, and describe how large `non-global' logarithms arise when we veto the energy…
We found that in transition arrays of complex atomic spectra, the strengths of electric-dipolar lines obey Benford's law, which means that their significant digits follow a logarithmic distribution favoring the smallest values. This…