Related papers: Symmetry in the Green's function for birth-death c…

The spectral relations for the four-time fermionic Green's functions are derived in the most general case. The terms which correspond to the zero-frequency anomalies, known before only for the bosonic Green's functions, are separated and…

We review some applications of self-consistent Green's function theory to studies of one- and two-nucleon structure in finite nuclei. Large-scale microscopic calculations that employ realistic nuclear forces are now possible. Effects of…

Consideration is given to the continuous-time supercritical branching random walk over a multidimensional lattice with a finite number of particle generation sources of the same intensity both with and without constraint on the variance of…

Using the approach suggested in [arXiv:1002.2761] we present below a sufficient condition guaranteeing that two collections of patterns of permutations have the same exponential generating functions for the number of permutations avoiding…

We revisit the computation of the discrete version of Schramm's formula for the loop-erased random walk derived by Kenyon. The explicit formula in terms of the Green function relies on the use of a complex connection on a graph, for which a…

We describe how to apply the recursive Green's function method to the computation of electronic transport properties of graphene sheets and nanoribbons in the linear response regime. This method allows for an amenable inclusion of several…

We prove for an arbitrary one-dimensional random walk with independent increments that the probability of crossing a level at a given time n has the order of square root of n. Moment or symmetry assumptions are not necessary. In removing…

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…

A second-order random walk on a graph or network is a random walk where transition probabilities depend not only on the present node but also on the previous one. A notable example is the non-backtracking random walk, where the walker is…

An integral relation is established between the Green functions corresponding to two Hamiltonians which are supersymmetric (SUSY) partners and in general may possess both discrete and continuous spectra. It is shown that when the continuous…

In this paper, we obtain the exact asymptotic behavior of Green functions of homogeneous random walks in $\Z^d$ killed at the first exit from and open cone of $\R^d$. Our approach combines methods of functional equations, integral…

We survey recent results on some one- and two-dimensional patterns generated by random permutations of natural numbers. In the first part, we discuss properties of random walks, evolving on a one-dimensional regular lattice in discrete time…

Non-Hermitian systems have garnered significant attention due to the emergence of novel topology of complex spectra and skin modes. However, investigating transport phenomena in such systems faces obstacles stemming from the non-unitary…

According to Comets, Gantert and Zeitouni on the one hand and to Derriennic on the other hand, some functionals associated to the hitting times of random walks in random environment on the integer line coincide, for the walk itself and for…

We introduce a transient reflected Brownian motion in a multidimensional orthant, which is either absorbed at the apex of the cone or escapes to infinity. We address the question of computing the absorption probability, as a function of the…

The Peierls bracket quantization scheme is applied to the supersymmetric system corresponding to the twisted spin index theorem. A detailed study of the quantum system is presented, and the Feynman propagator is exactly computed. The…

Motivated by the goal of understanding the evolution of populations undergoing selection, we consider branching Brownian motion in which particles independently move according to one-dimensional Brownian motion with drift, each particle may…

In this paper we are interested in obtaining the exact expression and the study of the constant sign of the Green's function related to a second order perturbed periodic problem coupled with integral boundary conditions at the extremes of…

Markov chains have long been used for generating random variates from spatial point processes. Broadly speaking, these chains fall into two categories: Metropolis-Hastings type chains running in discrete time and spatial birth-death chains…

Using the cluster expansions for n-point Green functions we derive a closed set of dynamical equations of motion for connected equal-time Green functions by neglecting all connected functions higher than $4^{th}$ order for the $\lambda…