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Now showing items 1-10 of 59

#### Wiener-Hopf Integral Equations in Mean First-passage Time Problems for Continuous-time Random Walks

(2023)

We study the mean first-passage time (MFPT) for asymmetric continuous time random walks in continuous space characterised by finite mean waiting times and jump amplitudes with both finite average and finite variance. We ...

#### Time Dynamics in Quantum Field Theory Systems

(2022-12-23)

In this doctoral thesis, we develop and investigate new mathematical tools that are intended to allow for a rigorous description of non–perturbative quantum field theory (QFT) dynamics. Here, the term QFT is to be understood ...

#### Exact calculation of the mean first-passage time of continuous-time random walks by nonhomogeneous Wiener-Hopf integral equations

(2022-12-23)

We study the mean first-passage time (MFPT) for asymmetric continuous-time random walks in continuous-space characterised by waiting-times with finite mean and by jump-sizes with both finite mean and finite variance. In ...

#### Statistical Characterization of Wildfire Dynamics: Studying the Relation Between Burned Area and Head of the Fire

(2022-06-06)

We show that the probability density function (PDF) of an area enclosed by a random perimeter is driven by the PDF of the integration bounds and the mean value of the perimeter function. With reference to wildfires, if the ...

#### Extended State Space for Describing Renormalized Fock Spaces in QFT

(2022-06-04)

In quantum field theory (QFT) models, it often seems natural to use, instead of wave functions from Fock space, wave functions that are not square-integrable and have prefactors involving divergent integrals (known as ...

#### Classical dynamics from self-consistency equations in quantum mechanics

(2022-05-09)

During the last three decades, P. Bóna has developed a non-linear generalization of quantum mechanics, based on symplectic structures for normal states and offering a general setting which is convenient to study the emergence ...

#### Implementing Bogoliubov Transformations Beyond the Shale-Stinespring Condition

(2022-04-28)

We provide two extensions of a dense subspace of Fock space, such that Bogoliubov transformations become implementable on them, even though they violate the Shale-Stinespring condition, so they are not implementable on ...

#### Linearization of holomorphic families of algebraic automor- phisms of the affine plane

(2022-01-03)

Let $G$ be a reductive group. We prove that a family of polynomial actions of $G$ on $\mathbb{C}^2$, holomorphically parametrized by an open Riemann surface, is linearizable. As an application, we show that a particular ...

#### Lower bounds on Hilbert-Kunz multiplicities and maximal F-signature

(2022)

ABSTRACT. Hilbert–Kunz multiplicity and F-signature are numerical invariants of commutative rings in positive characteristic that measure severity of singularities: for a regular ring both invariants are equal to one and ...

#### Uniform Lech's inequality

(2022)

Let (R,m) be a Noetherian local ring of dimension d ≥ 2. We prove that if e(Rred) > 1, then the classical Lech’s inequality can be improved uniformly for all m-primary ideals, that is, there exists ε > 0 such that e(I) ...