Recent Submissions

• The Abel map for surface singularities III: Elliptic germs ﻿

(2021-01-01)
The present note is part of a series of articles targeting the theory of Abel maps associated with complex normal surface singularities with rational homology sphere links (Nagy and Némethi in Math Annal 375(3):1427–1487, ...
• Delta invariant of curves on rational surfaces I. An analytic approach ﻿

(2021-01-01)
We prove that if (C, 0) is a reduced curve germ on a rational surface singularity (X, 0) then its delta invariant can be recovered by a concrete expression associated with the embedded topological type of the pair C X. ...
• High temperature convergence of the KMS boundary conditions: The Bose-Hubbard model on a finite graph ﻿

(2021-08-01)
The Kubo-Martin-Schwinger (KMS) condition is a widely studied fundamental property in quantum statistical mechanics which characterizes the thermal equilibrium states of quantum systems. In the seventies, Gallavotti and ...
• Parametrization simple irreducible plane curve singularities in arbitrary characteristic ﻿

(2020-01-01)
We study the classification of plane curve singularities in arbitrary characteristic. We first give a bound for the determinacy of a plane curve singularity with respect to pararametrization equivalence in terms of its ...
• Classification of Lipschitz simple function germs ﻿

(2020-07-01)
It was shown by Henry and Parusiński in 2003 that the bi-Lipschitz right equivalence of function germs admits moduli. In this article, we introduce the notion of Lipschitz simple function germ and present the complete ...
• Another Proof of Born's Rule on Arbitrary Cauchy Surfaces ﻿

(2021-10-14)
In 2017, Lienert and Tumulka proved Born's rule on arbitrary Cauchy surfaces in Minkowski space-time assuming Born's rule and a corresponding collapse rule on horizontal surfaces relative to a fixed Lorentz frame, as well ...
• Fractional Diffusion and Medium Heterogeneity: The Case of the Continuos Time Random Walk ﻿

(2021-07-24)
In this contribution we show that fractional diffusion emerges from a simple Markovian Gaussian random walk when the medium displays a power-law heterogeneity. Within the framework of the continuous time random walk, the ...
• Stochastic Properties of Colliding Hard Spheres in a Non-equilibrium Thermal Bath ﻿

(2021-07-24)
We consider the problem of describing the dynamics of a test particle moving in a thermal bath using the stochastic differential equations. We briefly recall the stochastic approach to the Brownian based on the statistical ...
• Image Milnor Number Formulas for Weighted-Homogeneous Map-Germs ﻿

(2021-07-05)
We give formulas for the image Milnor number of a weighted-homogeneous map-germ $(\mathbb{C}^n,0)\to(\mathbb{C}^{n+1},0)$, for $n=4$ and $5$, in terms of weights and degrees. Our expressions are obtained by a purely ...
• Classification of smooth factorial affine surfaces of Kodaira dimension zero with trivial units ﻿

(2021-07-31)
We give a corrected statement of (Gurjar and Miyanishi 1988, Theorem 2), which classifies smooth affine surfaces of Kodaira dimension zero, whose coordinate ring is factorial and has trivial units. Denote the class of such ...
• Some contributions to the theory of singularities and their characteristic classes ﻿

(2021-06-02)
In this Ph.D. thesis, we give some contributions to the theory of singularities, as well as to the theory of characteristic classes of singular spaces. The first part of this thesis is devoted to the theory of singularities ...
• Stochastic resetting by a random amplitude ﻿

(2021-05-18)
Stochastic resetting, a diffusive process whose amplitude is reset to the origin at random times, is a vividly studied strategy to optimize encounter dynamics, e.g., in chemical reactions. Here we generalize the resetting ...
• Macroscopic Dynamics of the Strong-Coupling BCS-Hubbard Model ﻿

(2020)
The aim of the current paper is to illustrate, in a simple example, our recent, very general, rigorous results on the dynamical properties of fermions and quantum-spin systems with long-range, or mean-field, interactions, ...
• Quantum Fluctuations and Large Deviation Principle for Microscopic Currents of Free Fermions in Disordered Media ﻿

(2020)
We contribute an extension of large-deviation results obtained in [N.J.B. Aza, J.-B. Bru, W. de Siqueira Pedra, A. Ratsimanetrimanana, J. Math. Pures Appl. 125 (2019) 209] on conductivity theory at atomic scale of free ...
• Weak* Hypertopologies with Application to Genericity of Convex Sets ﻿

(2022)
We propose a new class of hypertopologies, called here weak$^{\ast }$ hypertopologies, on the dual space $\mathcal{X}^{\ast }$ of a real or complex topological vector space $\mathcal{X}$. The most well-studied and well-known ...
• Large Deviations in Weakly Interacting Fermions - Generating Functions as Gaussian Berezin Integrals and Bounds on Large Pfaffians ﻿

(2021)
We prove that the G\"{a}rtner--Ellis generating function of probability distributions associated with KMS states of weakly interacting fermions on the lattice can be written as the limit of logarithms of Gaussian Berezin ...
• Exact distributions of the maximum and range of random diffusivity processes ﻿

(2021-02-09)
We study the extremal properties of a stochastic process $x_t$ defined by the Langevin equation ${\dot {x}}_{t}=\sqrt{2{D}_{t}}\enspace {\xi }_{t}$, in which $\xi_t$ is a Gaussian white noise with zero mean and $D_t$ is a ...
• Surrogate based Global Sensitivity Analysis of ADM1-based Anaerobic Digestion Model ﻿

(2021)
In order to calibrate the model parameters, Sensitivity Analysis routines are mandatory to rank the parameters by their relevance and fix to nominal values the least influential factors. Despite the high number of works ...
• Study of Wound Healing Dynamics by Single Pseudo-Particle Tracking in Phase Contrast Images Acquired in Time-Lapse ﻿

(2021-03)
Cellular contacts modify the way cells migrate in a cohesive group with respect to a free single cell. The resulting motion is persistent and correlated, with cells’ velocities self-aligning in time. The presence of a dense ...
• SHOULD I STAY OR SHOULD I GO? ZERO-SIZE JUMPS IN RANDOM WALKS FOR LÉVY FLIGHTS ﻿

(2021-02)
We study Markovian continuous-time random walk models for Lévy flights and we show an example in which the convergence to stable densities is not guaranteed when jumps follow a bi-modal power-law distribution that is equal ...