Related papers: Rough path properties for local time of symmetric …
We show that there is a polynomial-time algorithm with approximation guarantee $\frac{3}{2}+\epsilon$ for the $s$-$t$-path TSP, for any fixed $\epsilon>0$. It is well known that Wolsey's analysis of Christofides' algorithm also works for…
A statistic based on increment ratios (IR) and related to zero crossings of increment sequence is defined and studied for measuring the roughness of random paths. The main advantages of this statistic are robustness to smooth additive and…
We develop a complete path-integral formulation of relativistic quantum fields in local thermal equilibrium, which brings about the emergence of thermally induced curved spacetime. The resulting action is shown to have full diffeomorphism…
In this paper, we study the local linear convergence properties of a versatile class of Primal-Dual splitting methods for minimizing composite non-smooth convex optimization problems. Under the assumption that the non-smooth components of…
Completing a strategy of Gou\"ezel and Lalley, we prove a local limit theorem for the random walk generated by any symmetric finitely supported probability measure on a non-elementary Gromov-hyperbolic group: denoting by $R$ the inverse of…
Fix $p>1$, not necessarily integer, with $p(d-2)<d$. We study the $p$-fold self-intersection local time of a simple random walk on the lattice $\Z^d$ up to time $t$. This is the $p$-norm of the vector of the walker's local times, $\ell_t$.…
Motivated by the recent advances in the theory of stochastic partial differential equations involving nonlinear functions of distributions, like the Kardar-Parisi-Zhang (KPZ) equation, we reconsider the unique solvability of one-dimensional…
An essential feature of the subdiffusion equations with the $\alpha$-order time fractional derivative is the weak singularity at the initial time. The weak regularity of the solution is usually characterized by a regularity parameter…
We study the existence and regularity of local times for general $d$-dimensional stochastic processes. We give a general condition for their existence and regularity properties. To emphasize the contribution of our results, we show that…
An instance of the NP-hard Quadratic Shortest Path Problem (QSPP) is called linearizable iff it is equivalent to an instance of the classic Shortest Path Problem (SPP) on the same input digraph. The linearization problem for the QSPP…
Understanding which physical processes are symmetric with respect to time inversion is a ubiquitous problem in physics. In quantum physics, effective gauge fields allow emulation of matter under strong magnetic fields, realizing the…
We consider the problem of inference for non-stationary time series with heavy-tailed error distribution. Under a time-varying linear process framework we show that there exists a suitable local approximation by a stationary process with…
The quantized canonical space-time coordinates of a relativistic point particle are expressed in terms of the elements of a complex Clifford algebra which combines the complex properties of SL(2.C) and quantum mechanics. When the quantum…
Power law generalized covariance functions provide a simple model for describing the local behavior of an isotropic random field. This work seeks to extend this class of covariance functions to spatial-temporal processes for which the…
We formulate indefinite integration with respect to an irregular function as an algebraic problem and provide a criterion for the existence and uniqueness of a solution. This allows us to define a good notion of integral with respect to…
We provide a unified analytic approach to study stationary states of controlled differential equations driven by rough paths, using the framework of random dynamical systems and random attractors. Part I deals with driving paths of finite…
Study of stochastic differential equations on the field of p-adic numbers was initiated by the second author and has been developed by the first author, who proved several results for the p-adic case, similar to the theory of ordinary…
This article shows an It\^o-Wentzell type formula adapted to rough paths with $\alpha$-H\"older regularity $\alpha \in (\frac{1}{3},\frac{1}{2}]$. We improve previous results of R. Castrequini and P. Catuogno for the Young integral and C.…
Starting from the canonical formalism of relativistic (timeless) quantum mechanics, the formulation of timeless path integral is rigorously derived. The transition amplitude is reformulated as the sum, or functional integral, over all…
If the coupling constants in QFT are promoted to functions of space-time, the dependence of the path integral on these couplings is highly constrained by conformal symmetry. We begin the present note by showing that this idea leads to a new…