Related papers: Another probabilistic construction of ${\Phi}^{2n}…
We obtain alternative expressions for the multigraviton tree level amplitudes and discuss their general properties. In particular, by analogy with Yang-Mills theory, we find that some combinatoric structure can be carried by a Chan-Paton…
We use a new eigenvalue concentration bound for the fluctuation of the sample mean of the random extternal potential in the multi-particle Anderson model and prove the spectral exponential and the strong dynamical localization. The results…
This paper presents an approach for the modelling of dependent random variables using generalised polynomial chaos. This allows to write chance-constrained optimization problems with respect to a joint distribution modelling dependencies…
We consider random polynomials of the form $G_n(z):= \sum_{|\alpha|\leq n} \xi^{(n)}_{\alpha}p_{n,\alpha}(z)$ where $\{\xi^{(n)}_{\alpha}\}_{|\alpha|\leq n}$ are i.i.d. (complex) random variables and $\{p_{n,\alpha}\}_{|\alpha|\leq n}$ form…
We extend the key formula which intertwines multiplicative Markoff-Lagrange spectrum and symbolic dynamics. The proof uses complex analysis and elucidates the strategy of the problem. Moreover, the new method applies to a wide variety of…
The new Theorem on location of maximum of probability density functions of dimensionless second difference of the three adjacent energy levels for $N$-dimensional Gaussian orthogonal ensemble GOE($N$), $N$-dimensional Gaussian unitary…
We consider a fractional nonlinear wave equations (fNLW) with a general power-type nonlinearity, on the two-dimensional torus. Our main goal is to construct invariant global-in-time Gibbs dynamics for a renormalized fNLW. We first construct…
Rational solutions and special polynomials associated with the generalized K_2 hierarchy are studied. This hierarchy is related to the Sawada-Kotera and Kaup-Kupershmidt equations and some other integrable partial differential equations…
For the special case of compact QED in (2+1) dimensions, we calculate the non-Gaussian vacuum wave-functional to second order in the monopole fugacity and obtain the effective photon mass. Our method presents some hope for understanding the…
Extending the usual Ginzburg-Landau theory for the random-field Ising model, the possibility of dimensional reduction is reconsidered. A renormalization group for the probability distribution of magnetic impurities is applied. New…
We recently constructed a causal quantum mechanics in 2 dim. phase space which is more realistic than the de Broglie-Bohm mechanics as it reproduces not just the position but also the momentum probability density of ordinary quantum theory.…
We study the top Lyapunov exponent of a product of random $2 \times 2$ matrices appearing in the analysis of several statistical mechanical models with disorder, extending a previous treatment of the critical case (Giacomin and Greenblatt,…
We extract the long-range gravitational potential between two scalar particles with arbitrary masses from the two-to-two elastic scattering amplitude at 2nd Post-Minkowskian order in arbitrary dimensions. In contrast to the four-dimensional…
Approximations based on two-particle irreducible (2PI) effective actions (also known as $\Phi$-derivable, Cornwall-Jackiw-Tomboulis or Luttinger-Ward functionals depending on context) have been widely used in condensed matter and…
In this work the interplay between matrix biorthogonal polynomials with respect to a matrix of linear functionals, the $k$-th associated matrix polynomials and the second kind matrix functions, is studied in terms of quasideterminants. A…
We consider in this note a class of two-dimensional determinantal Coulomb gases confined by a radial external field. As the number of particles tends to infinity, their empirical distribution tends to a probability measure supported in a…
The structure of classical electrodynamics based on the variational principle together with causality and space-time homogeneity is analyzed. It is proved that in this case the 4-potentials are defined uniquely. On the other hand, the…
Consider a quadratic polynomial $f\left(\xi_{1},\dots,\xi_{n}\right)$ of independent Bernoulli random variables. What can be said about the concentration of $f$ on any single value? This generalises the classical Littlewood--Offord problem,…
This review is devoted to the detailed consideration of the universal statistical properties of one-dimensional directed polymers in a random potential. In terms of the replica Bethe ansatz technique we derive several exact results for…
Using connection with quantum field theory, the infinitesimal covariant abelian gauge transformation laws of relativistic two-particle constraint theory wave functions and potentials are established and weak invariance of the corresponding…