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Concentration Inequalities for Output Statistics of Quantum Markov Processes
We derive new concentration bounds for time averages of measurement outcomes in quantum Markov processes. This generalizes well-known bounds for...
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Optimal Thermodynamic Uncertainty Relation in Markov Jump Processes
We investigate the tightness and optimality of thermodynamic-uncertainty-relation (TUR)-type inequalities from two aspects, the choice of the Fisher...
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On the non-Markovianity of quantum semi-Markov processes
The non-Markovianity of the stochastic process called the quantum semi-Markov (QSM) process is studied using a recently proposed quantification of...
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Effective Hamiltonians and Lagrangians for Conditioned Markov Processes at Large Volume
When analysing statistical systems or stochastic processes, it is often interesting to ask how they behave given that some observable takes some...
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From Semi-Markov Random Evolutions to Scattering Transport and Superdiffusion
We here study random evolutions on Banach spaces, driven by a class of semi-Markov processes. The expectation (in the sense of Bochner) of such...
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The Vanishing of Excess Heat for Nonequilibrium Processes Reaching Zero Ambient Temperature
We present the mathematical ingredients for an extension of the Third Law of Thermodynamics (Nernst heat postulate) to nonequilibrium processes. The...
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Stochastic Processes
In this chapter, we lay the foundation of stochastic processes. We start with a general definition of a stochastic process, and then specialize to...
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A new definition of hitting time and an embedded Markov chain in continuous-time quantum walks
We present a new probabilistic definition for the hitting time of a continuous-time quantum walk into a marked set of nodes, when measurements with...
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Optimal Control of Stochastic Processes
Many control problems appearing for complex systems are subject to imperfectly known disturbances. As we have learned in the previous chapter, these...
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Stochastic Processes
In this chapter, we introduce a mathematical framework, stochastic processes, which is used to describe small stochastic systems.
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Non-reversible Metastable Diffusions with Gibbs Invariant Measure II: Markov Chain Convergence
This article considers a class of metastable non-reversible diffusion processes whose invariant measure is a Gibbs measure associated with a Morse...
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Revisiting the universal texture zero of flavour: a Markov chain Monte Carlo analysis
We revisit the phenomenological predictions of the Universal Texture Zero (UTZ) model of flavour originally presented in [
1 ], and update them in...
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Modified Log-Sobolev Inequality for a Compact Pure Jump Markov Process with Degenerate Jumps
We study the modified log-Sobolev inequality for a class of pure jump Markov processes that describe the interactions between brain neurons. As a...
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Kardar–Parisi–Zhang Equation from Long-Range Exclusion Processes
We prove here that the height function associated to non-simple exclusion processes with arbitrary jump-length converges to the solution of the...
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Derivation of a nonequilibrium Markov six-state model in the presence of a time-reversal antisymmetric variable
A Markov model that does not satisfy the detailed balance condition is often used for modeling a system continuously driven out of equilibrium by an...
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Low-Lying Eigenvalues and Convergence to the Equilibrium of Some Piecewise Deterministic Markov Processes Generators in the Small Temperature Regime
In this work, we study the number of small eigenvalues and the convergence to the equilibrium of the Bouncy Particle Sampler process and the zigzag...
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Visualizing Markov Process Through Graphs and Trees
In this chapter, we use the concept of a Markov chain to define the stochastic processes and broadly frame its fundamentals for our methods. This...
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Some Poisson-Based Processes at Geometric Times
We consider the composition of three different stochastic processes with an independent geometric random time. First, the parent process is assumed...
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Stochastic Processes in Continuous Space
In this chapter, we consider a stochastic particle in continuous space. A prominent example is a Brownian particle, which is briefly explained at the...