Czech Academy of Sciences, Institute of Mathematics

Viscosity Supersolution Barriers to a Non-local Free Boundary Problem

We study a parabolic obstacle partial integro-differential equation with a dynamically moving bilateral free boundary. This type of problem arises in the mathematical modeling of speculative asset bubbles with L\'evy jump processes. We investigate the existence of viscosity super...

Asymptotic stability and cut-off phenomenon for the underdamped Langevin dynamics

In this article, we provide a detailed analysis of the long-time behavior of the underdamped Langevin dynamics. We first provide a necessary condition guaranteeing that the zero-noise dynamical system converges to its unique attractor. We also observed that this condition is shar...

Monotonicity, topology, and convexity of recurrence in random walks

We consider nonhomogeneous random walks on the two-dimensional positive quadrant N2. In the 1960’s the following question was asked for N2: is it true if such a random walk X is recurrent and Y is another random walk that at every point is more likely to go down and more likely t...

Alon–Tarsi for Hypergraphs

Given a hypergraph $H=(V, E)$, define for every edge $e\in E$ a linear expression with arguments corresponding to the vertices. Next, let the polynomial $p_H$ be the product of such linear expressions for all edges. Our main goal is to find a relationship between the Alon-Tarsi n...

The Hardy averaging operator between Orlicz spaces and a new gauge functional characterizing a given Orlicz space

Abstract We prove that the largest Orlicz space into which the Hardy averaging operator maps coincides with the largest rearrangement-invariant (r.i.) space mapping into that space; in other words, the optimal Orlicz domain is automatically the optimal r.i. domain. More generally...

Convergence Analysis of a Numerical Algorithm for Spatial Segregation of Two Population Densities

Over the last few decades, the numerical approximation of spatial segregation equations for reaction-diffusion systems with $m$ population densities has gained significant interest. These problems are governed by a minimization problem subject to a closed but non-convex set. In t...

Law Equivalence for Ornstein–Uhlenbeck Dynamics Driven by Lévy Noise

For stochastic partial differential equations driven by Lévy noise, understanding when changes in the drift operator preserve the law of the solution is fundamental to filtering, control, and simulation. We extend law-comparison results for Ornstein–Uhlenbeck processes from bound...

Fluctuations of Schensted row insertion

We investigate asymptotic probabilistic phenomena arising from the application of the Schensted row insertion algorithm, a key component of the Robinson–Schensted–Knuth (RSK) correspondence, to random inputs. Our analysis centers on a random tableau T with a given shape λ, which...

A note on multivariate diam-mean equicontinuity and frequent stability

Abstract Let <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mi>X</mml:mi> <mml:mo>,</mml:mo> <mml:mi>G</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:math> be a topological dynamical...

Hamana’s injective envelope as a maximal rigid multiplier cover

Abstract Let A be a unital $$C^*$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>C</mml:mi> <mml:mo>∗</mml:mo> </mml:msup> </mml:math> -algebra. An A -multiplier cover is a $$C^*$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup>...