Related papers: The generating function for total displacement
We define a class of divergences to measure differences between probability density functions in one-dimensional sample space. The construction is based on the convex function with the Jacobi operator of mapping function that pushforwards…
An intermittent nonlinear map generating subdiffusion is investigated. Computer simulations show that the generalized diffusion coefficient of this map has a fractal, discontinuous dependence on control parameters. An amended continuous…
We present a generalized optimal transport model in which the mass-preserving constraint for the $L^2$-Wasserstein distance is relaxed by introducing a source term in the continuity equation. The source term is also incorporated in the path…
We analyze the statistical physics of self-propelled particles from a general theoretical framework that properly describes the most salient characteristic of active motion, $persistence$, in arbitrary spatial dimensions. Such a framework…
We introduce a new universality class of one-dimensional iteration model giving rise to self-similar motion, in which the Feigenbaum constants are generalized as self-similar rates and can be predetermined. The curves of the mean-square…
In an exercise in the first volume of his famous series of books, Knuth considered sorting permutations by passing them through a stack. Many variations of this exercise have since been considered, including allowing multiple passes through…
We consider weighted small step walks in the positive quadrant, and provide algebraicity and differential transcendence results for the underlying generating functions: we prove that depending on the probabilities of allowed steps, certain…
In this thesis massive higher derivative gravity theories are analyzed in some detail. One-particle scattering amplitude between two covariantly conserved sources mediated by a graviton exchange is found at tree-level in $D$ dimensional…
We consider first passage percolation on sparse random graphs with prescribed degree distributions and general independent and identically distributed edge weights assumed to have a density. Assuming that the degree distribution satisfies a…
Geometric Brownian motion (GBM) is a key model for representing self-reproducing entities. Self-reproduction may be considered the definition of life [5], and the dynamics it induces are of interest to those concerned with living systems…
The 1+1 dimensional corner growth model with exponential weights is a centrally important exactly solvable model in the Kardar-Parisi-Zhang class of statistical mechanical models. While significant progress has been made on the fluctuations…
Let G be a group, and let M=(m_n) be a sequence of finitely supported probability measures on G. Consider the probability that two elements chosen independently according to m_n commute. Antolin, Martino and Ventura define the 'degree of…
We analyze a class of continuous time random walks in $\mathbb R^d,d\geq 2,$ with uniformly distributed directions. The steps performed by these processes are distributed according to a generalized Dirichlet law. Given the number of changes…
We consider a finite quantum system coupled to quasifree thermal reservoirs at different temperatures. Under the assumptions of small coupling and exponential decay of the reservoir correlation function, the large deviation generating…
Propulsion of otherwise passive objects is achieved by mechanisms of active driving. We concentrate on cases in which the direction of active drive is subject to spontaneous symmetry breaking. In our case, this direction will be maintained,…
Crystal plasticity is the result of the motion and interaction of dislocations. There is, however, still a major gap between microscopic and mesoscopic simulations and continuum crystal plasticity models. Only recently a higher dimensional…
We study families of partitions with gap conditions that were introduced by Schur and Andrews, and describe their fundamental connections to combinatorial q-series and automorphic forms. In particular, we show that the generating functions…
We study the arithmetic Fourier transforms of trace functions on general connected commutative algebraic groups. To do so, we first prove a generic vanishing theorem for twists of perverse sheaves by characters, and using this tool, we…
It is known that the generating function associated with the enumeration of non-backtracking walks on finite graphs is a rational matrix-valued function of the parameter; such function is also closely related to graph-theoretical results…
We study $I(T)$, the number of inversions in a tree $T$ with its vertices labeled uniformly at random, which is a generalization of inversions in permutations. We first show that the cumulants of $I(T)$ have explicit formulas involving the…