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We study Markov chains on $\mathbb Z^m$, $m\geq 2$, that behave like a standard symmetric random walk outside of the hyperplane (membrane) $H=\{0\}\times \mathbb Z^{m-1}$. The transition probabilities on the membrane $H$ are periodic and…
Upper bounds of the Hausdorff volume of scalar gradient field graphs are derived by means of geometric measure theory. The approach reproduces that scalar gradient fields along a mean imposed scalar gradient become space filling for…
The effective geometry and the gravitational coupling of nonabelian gauge and scalar fields on generic NC branes in Yang-Mills matrix models is determined. Covariant field equations are derived from the basic matrix equations of motions,…
This paper describes recent progress in the analysis of relativistic gauge conditions for Euclidean Maxwell theory in the presence of boundaries. The corresponding quantum amplitudes are studied by using Faddeev-Popov formalism and…
Langevin dynamics has found a large number of applications in sampling, optimization and estimation. Preconditioning the gradient in the dynamics with the covariance - an idea that originated in literature related to solving estimation and…
In principle, observables as for example the sphaleron rate or the tunneling rate in a first-order phase transition are gauge-independent. However, in practice a gauge dependence is introduced in explicit perturbative calculations due to…
We prove that the rescaled ``true'' self-avoiding walk $(n^{-2/3}X_{\lfloor nt \rfloor})_{t\in\mathbb{R}_+}$ converges weakly as $n$ goes to infinity to the ``true'' self-repelling motion constructed by T\'oth and Werner. The proof features…
The influence of a random environment on the dynamics of a fluctuating rough surface is investigated using a field theoretic renormalization group. The environment motion is modelled by the stochastic Navier--Stokes equation, which includes…
We define natural probability measures on cycle-rooted spanning forests (CRSFs) on graphs embedded on a surface with a Riemannian metric. These measures arise from the Laplacian determinant and depend on the choice of a unitary connection…
We prove that the dimension drop phenomenon holds for the harmonic measure associated to a transient random walk in a random environment (as defined by R. Lyons and R. Pemantle in 1992 and generalized by G. Faraud in 2011) on an infinite…
We consider the multi-time correlation and covariance structure of a random surface growth with a wall introduced in arXiv:0904.2607. It is shown that the correlation functions associated with the model along space-like paths have…
We study a class of discrete-time random walks in $\mathbb{R}^d$ whose conditional drift decays polynomially in time and grows polynomially with the distance from the origin to the current position. This class is related to several models…
We study here a detailed conjecture regarding one of the most important cases of anomalous diffusion, i.e the behavior of the "ant in the labyrinth". It is natural to conjecture (see [16] and [8]) that the scaling limit for random walks on…
We consider an extended scalar-tensor theory of gravity where the action has two interacting scalar fields, a Brans-Dicke field which makes the effective Newtonian constant a function of coordinates and a Higgs field which has derivative…
In this note we first consider local times of random walks killed at leaving positive half-axis. We prove that the distribution of the properly rescaled local time at point $N$ conditioned on being positive converges towards an exponential…
We compute explicit upper bounds on the distance between the law of a multivariate Gaussian distribution and the joint law of wavelets/needlets coefficients based on a homogeneous spherical Poisson field. In particular, we develop some…
We show how it is possible to assess the rate of convergence in the Gaussian approximation of triangular arrays of $U$-statistics, built from wavelets coefficients evaluated on a homogeneous spherical Poisson field of arbitrary dimension.…
In this paper, we continue the study of large $N$ problems for the Wick renormalized linear sigma model, i.e. $N$-component $\Phi^4$ model, in two spatial dimensions, using stochastic quantization methods and Dyson--Schwinger equations. We…
We show that the two-point function \sigma(x,x')=\sqrt{<[\phi(x)-\phi(x')]^{2}>} of a scalar quantum field theory is a metric (i.e., a symmetric positive function satisfying the triangle inequality) on space-time (with imaginary time). It…
We generalize the Rayleigh Quotient Iteration (RQI) to the problem of solving a nonlinear equation where the variables are divided into two subsets, one satisfying additional equality constraints and the other could be considered as…