We propose a resolution of the discrepancy between the proton yield predicted by the statistical hadronization approach and data on hadron production in ultra-relativistic nuclear collisions at the LHC. Applying the S-matrix formulation of statistical mechanics to include pion-nucleon interactions, we reexamine their contribution to the proton yield, taking resonance widths and the presence of nonresonant correlations into account. The effect of multi-pion-nucleon interactions is estimated using lattice QCD results on the baryon-charge susceptibility. We show that a consistent implementation of these features in the statistical hadronization model, leads to a reduction of the predicted proton yield, which then quantitatively matches data of the ALICE collaboration for Pb-Pb collisions at the LHC.

The study of Eu intermetallic compounds has allowed the exploration of valence fluctuations and transitions in 4f electron systems. Recently, a Eu$_2$Pt$_6$Al$_{15}$ phase synthesized by arc-melting followed by a thermal treatment was reported [M. Radzieowski \textit{et al.}, J Am Chem Soc 140(28), 8950-8957 (2018)], which undergoes a transition upon cooling below 45~K that was interpreted as a valence transition from Eu$^{2+}$ to Eu$^{3+}$. In this paper, we present the discovery of another polymorph of Eu$_2$Pt$_6$Al$_{15}$ obtained by high-temperature solution growth, that presents different physical properties than the arc-melted polycrystalline sample. Despite the similarities in crystal structure and chemical composition, the Eu valence transition is almost fully suppressed in the solution-grown crystals, allowing the moments associated with the Eu$^{2+}$ state to order antiferromagnetically at around 14~K. A detailed analysis of the crystal structure using single crystal X-ray diffraction reveals that, although the solution grown crystals are built from the same constituent layers as the arc-melted samples, these layers present a different stacking. The effect of different thermal treatments is also studied. Different anneal procedures did not result in significant changes of the intrinsic properties, and only by arc-melting and quenching the crystals we were able to convert them into the previously reported polymorph.

There are two modes by which clusters of aggregating particles can coalesce: The clusters can merge either (i) by the Ostwald ripening process in which particles diffuse from one cluster to the other whilst the cluster centres remain stationary, or (ii) by means of a cluster translation mode, in which the clusters move towards each other and join. To understand in detail the interplay between these different modes, we study a model system of hard particles with an additional attraction between them. The particles diffuse along narrow channels with smooth or periodically corrugated walls, so that the system may be treated as one-dimensional. When the attraction between the particles is strong enough, they aggregate to form clusters. The channel potential influences whether clusters can move easily or not through the system and can prevent cluster motion. We use Dynamical Density Functional theory to study the dynamics of the aggregation process, focusing in particular on the coalescence of two equal size clusters. As long as the particle hard-core diameter is non-zero, we find that the coalescence process can be halted by a sufficiently strong corrugation potential. The period of the potential determines the size of the final stable clusters. For the case of smooth channel walls, we demonstrate that there is a cross-over in the dominance of the two different coarsening modes, that depends on the strength of the attraction between particles, the cluster sizes and the separation distance between clusters.

We report on a measurement of elastic electron scattering on argon performed with a novel cryogenic gas-jet target at the Mainz Microtron accelerator MAMI. The luminosity is estimated with the thermodynamical parameters of the target and by comparison to a calculation in distorted-wave Born approximation. The cross section, measured at new momentum transfers of 1.24 fm$^{-1}$ and 1.55 fm$^{-1}$ is in agreement with previous experiments performed with a traditional high-pressure gas target, as well as with modern ab-initio calculations employing state-of-the-art nuclear forces from chiral effective field theory. The nearly background-free measurement highlights the optimal properties of the gas-jet target for elements heavier than hydrogen, enabling new applications in hadron and nuclear physics.

We propose a resolution of the discrepancy between the proton yield predicted by the statistical hadronization approach and data on hadron production in ultra-relativistic nuclear collisions at the LHC. Applying the S-matrix formulation of statistical mechanics to include pion-nucleon interactions, we reexamine their contribution to the proton yield, taking resonance widths and the presence of nonresonant correlations into account. The effect of multi-pion-nucleon interactions is estimated using lattice QCD results on the baryon-charge susceptibility. We show that a consistent implementation of these features in the statistical hadronization model, leads to a reduction of the predicted proton yield, which then quantitatively matches data of the ALICE collaboration for Pb-Pb collisions at the LHC.

We study a real symmetric $\Phi^4$-matrix model whose kinetic term is given by $\mathrm{Tr}( E \Phi^2)$, where $E$ is a positive diagonal matrix without degenerate eigenvalues. We show that the partition function of this matrix model corresponds to a zero-energy solution of a Schödinger type equation with Calogero-Moser Hamiltonian. A family of differential equations satisfied by the partition function is also obtained from the Virasoro algebra.

It is shown that rational points over finite fields of moduli spaces of stable quiver representations are counted by polynomials with integer coefficients. These polynomials are constructed recursively using an identity in the Hall algebra of a quiver.

We construct and study properties of an infinite dimensional analog of Kahane's theory of Gaussian multiplicative chaos \cite{K85}. Namely, if $H_T(\omega)$ is a random field defined w.r.t. space-time white noise $\dot B$ and integrated w.r.t. Brownian paths in $d\geq 3$, we consider the renormalized exponential, weighted w.r.t. the Wiener measure $\mathbb P_0$. We construct the almost sure limit $\mu_\gamma$ in the {\it entire weak disorder (subcritical)} regime and call it {\it subcritical GMC} on the Wiener space. We show that $$\mu_\gamma\Big\{\omega: \lim_{T\to\infty} \frac{H_T(\omega)}{T(\phi\star\phi)(0)} \ne \gamma\Big\}=0 \qquad \mbox{almost surely,}$$ meaning, $\mu_\gamma$ is supported only on $\gamma$-{\it thick paths}, and consequently, the normalized version is singular w.r.t. the Wiener measure. We characterize uniquely the limit $\mu_\gamma$ w.r.t. the mollification scheme $\phi$ in the sense of Shamov \cite{S14} and the random {\it rooted} measure $\mathbb Q_{\mu_\gamma}(d\dot B d\omega)= \mu_\gamma(d\omega,\dot B)P(d\dot B)$. We then determine the fractal properties of the measure around $\gamma$-thick paths: -C_2 \leq \liminf_{r\to 0} r^2 \log \widehat\mu_\gamma(\|\omega\| < r) \leq \limsup_{r\to 0}\sup_\eta r^2 \log \widehat\mu_\gamma(\|\omega-\eta \| < r) \leq -C_1 w.r.t a weighted norm $\|\cdot\|$. Here C_1>0 and C_2<\infty are the uniform upper (resp. pointwise lower) Hölder exponents which are {\it explicit} in the entire weak disorder regime. Moreover, they converge to the scaling exponent of the Wiener measure as the disorder approaches zero. Finally, we establish negative and $L^p$ (p>1) moments for the total mass of $\mu_\gamma$ in the weak disorder regime.

We show that a negative Einstein manifold admitting a proper isometric action of a connected unimodular Lie group with compact, possibly singular, orbit space splits isometrically as a product of a symmetric space and a compact negative Einstein manifold. The proof involves the theory of polar actions, Lie-theoretic arguments and maximum principles.

One-flavour QCD - a gauge theory with SU(3) colour gauge group and a fermion in the fundamental representation - is studied by Monte Carlo simulations. The mass spectrum of hadronic bound states is investigated in a volume with extensions of L ~ 4.4r_0 (~2.2fm) at two different lattice spacings: a ~ 0.37r_0 (~0.19fm) and a ~ 0.27r_0 (~0.13fm). The lattice action is Symanzik tree-level-improved Wilson action for the gauge field and (unimproved) Wilson action for the fermion.

Let $\mathcal G$ be the Cayley graph of a finitely generated, infinite group $\Gamma$. We show that $\Gamma$ has the Haagerup property if and only if for every \alpha<1, there is a $\Gamma$-invariant bond percolation $\mathbb P$ on $\mathcal G$ with \mathbb E[\mathrm{deg}_{\omega}(g)]>\alpha\mathrm{deg}_{\mathcal G}(g) for every vertex $g$ and with the two-point function $\tau(g,h)=\mathbb P\big[g\leftrightarrow h\big]$ vanishing as $d(g,h)\to\infty$. On the other hand, we show that $\Gamma$ has Kazhdan's property (T) if and only if there exists a threshold \alpha^*<1 such that for every $\Gamma$-invariant bond percolation $\mathbb P$ on $\mathcal G$, \mathbb E[\mathrm{deg}_\omega(o)]>\alpha^*\mathrm{deg}(o) implies that the two-point function is uniformly bounded away from zero. These results in particular answer questions raised by Lyons (J. Math. Phys. 41. 1099-1126 (2000)) about characterizations of properties of groups beyond amenability through group-invariant percolations. The method of proof is new and is based on a construction of percolations with suitable dependence structures built from invariant point processes on spaces with measured walls. This construction furthermore leads to quantitative bounds on the two-point functions, exhibiting in particular exponential decay of the two-point function in several prominent examples of Haagerup groups, including co-compact Fuchsian groups, co-compact discrete subgroups of $\mathrm{Isom}(\mathbb H^n)$ and lamplighters over free groups. This method also allows us to extend the aforementioned characterization of property (T) to the setting of relative property (T) and provide an application to Bernoulli percolation at the uniqueness threshold.

We prove a priori bounds for solutions of singular stochastic porous media equations with multiplicative noise in their natural $L^1$-based regularity class. We consider the first singular regime, i.e.~noise of space-time regularity $\alpha-2$ for $\alpha\in(2/3,1)$, and prove modelledness of the solution in the sense of regularity structures with respect to the solution of the corresponding linear stochastic heat equation. The proof relies on the kinetic formulation of the equation and a novel renormalized energy inequality. A careful analysis allows to balance the degeneracy of the diffusion coefficient against sufficiently strong damping of the multiplicative noise for small values of the solution.

The Fourier harmonics, $v_2$ and $v_3$ of negative pions are measured at center-of-mass energy per nucleon pair of $\sqrt{s_{\mathrm{NN}}}$= 17.3 GeV around midrapidity by the CERES/NA45 experiment at the CERN SPS in 0--30\% central PbAu collisions with a mean centrality of 5.5\%. The analysis is performed in two centrality bins as a function of the transverse momentum $\mathrm{p_{\mathrm{T}}}$ from 0.05 GeV/$c$ to more than 2 GeV/$c$. This is the first measurement of the $v^{1/3}_{3}/v^{1/2}_{2}$ ratio as a function of transverse momentum at SPS energies, that reveals, independently of the hydrodynamic models, hydrodynamic behavior of the formed system. For $\mathrm{p_{\mathrm{T}}}$ above 0.5 GeV/$c$, the ratio is nearly flat in accordance with the hydrodynamic prediction and as previously observed by the ATLAS and ALICE experiments at the much higher LHC energies. The results are also compared with the SMASH-vHLLE hybrid model predictions, as well as with the SMASH model applied alone.

The paper reports on the improved Mainz experiment on tritum $\beta$ spectroscopy which yields a 10 times' higher signal to background ratio than before. The main experimental effects and systematic uncertainties have been investigated in side experiments and possible error sources have been eliminated. Extensive data taking took place in the years 1997 to 2001. A residual analysis of the data sets yields for the square of the electron antineutrino mass the final result of $m^2(\nu_e)=(-0.6 \pm 2.2_{\rm{stat}} \pm 2.1_{\rm{syst}})$ eV$^2$/c$^4$. We derive an upper limit of $m(\nu_e)\leq 2.3$ eV/c$^2$ at 95% confidence level for the mass itself.

We report a quasi-differential upper limit on the extremely-high-energy (EHE) neutrino flux above $5\times 10^{6}$ GeV based on an analysis of nine years of IceCube data. The astrophysical neutrino flux measured by IceCube extends to PeV energies, and it is a background flux when searching for an independent signal flux at higher energies, such as the cosmogenic neutrino signal. We have developed a new method to place robust limits on the EHE neutrino flux in the presence of an astrophysical background, whose spectrum has yet to be understood with high precision at PeV energies. A distinct event with a deposited energy above $10^{6}$ GeV was found in the new two-year sample, in addition to the one event previously found in the seven-year EHE neutrino search. These two events represent a neutrino flux that is incompatible with predictions for a cosmogenic neutrino flux and are considered to be an astrophysical background in the current study. The obtained limit is the most stringent to date in the energy range between $5 \times 10^{6}$ and $5 \times 10^{10}$ GeV. This result constrains neutrino models predicting a three-flavor neutrino flux of $E_\nu^2\phi_{\nu_e+\nu_\mu+\nu_\tau}\simeq2\times 10^{-8}\ {\rm GeV}/{\rm cm}^2\ \sec\ {\rm sr}$ at $10^9\ {\rm GeV}$. A significant part of the parameter-space for EHE neutrino production scenarios assuming a proton-dominated composition of ultra-high-energy cosmic rays is excluded.

We show that a locally finite, connected graph has a coarse embedding into a Hilbert space if and only if there exist bond percolations with arbitrarily large marginals and two-point function vanishing at infinity. We further show that the decay of the two-point function is stretched exponential with stretching exponent $\alpha\in[0,1]$ if and only if the $L^1$-compression exponent of the graph is at least $\alpha$, leading to a probabilistic characterization of this exponent. These results are new even in the particular setting of Cayley graphs of finitely generated groups. The proofs build on new probabilistic methods introduced recently by the authors to study group-invariant percolation on Cayley graphs [25,26], which are now extended to the general, non-symmetric situation of graphs to study their coarse embeddability and $L^1$-compression exponents.

This is the main paper of a series establishing the linear stability of Schwarzschild-Anti-de Sitter (AdS) black holes to gravitational perturbations. Specifically, we prove that solutions to the linearisation of the Einstein equations $\textrm{Ric}(g) = \Lambda g$ with \Lambda<0 around a Schwarzschild-AdS metric arising from regular initial data and with standard Dirichlet-type boundary conditions imposed at the conformal boundary (inherited from fixing the conformal class of the non-linear metric) remain globally uniformly bounded on the black hole exterior and in fact decay inverse logarithmically in time to a linearised Kerr-AdS metric. The proof exploits a hierarchical structure of the equations of linearised gravity in double null gauge and crucially relies on boundedness and logarithmic decay results for the Teukolsky system, which are independent results proven in Part II of the series. Contrary to the asymptotically flat case, addition of a residual pure gauge solution to the original solution is not required to prove decay of all linearised null curvature and Ricci coefficients. One may however normalise the solution at the conformal boundary to be in standard AdS-form by adding such a pure gauge solution, which is constructed dynamically from the trace of the original solution at the conformal boundary and quantitatively controlled by initial data.

A Hermitian $\Phi^4$ matrix model with a Kontsevich-type kinetic term is studied. It was recently discovered that the partition function of this matrix model satisfies the Schrödinger equation of the $N$-body harmonic oscillator, and that eigenstates of the Virasoro operators can be derived from this partition function. We extend these results and obtain an explicit formula for such eigenstates in terms of the free energy. Furthermore, the Schrödinger equation for the $N$-body harmonic oscillator can also be reformulated in terms of connected correlation functions. The $U(1)^N$-symmetry allows us to derive loop equations.

Nonparametric Bayesian approaches based on Gaussian processes have recently become popular in the empirical learning community. They encompass many classical methods of statistics, like Radial Basis Functions or various splines, and are technically convenient because Gaussian integrals can be calculated analytically. Restricting to Gaussian processes, however, forbids for example the implemention of genuine nonconcave priors. Mixtures of Gaussian process priors, on the other hand, allow the flexible implementation of complex and situation specific, also nonconcave "a priori" information. This is essential for tasks with, compared to their complexity, a small number of available training data. The paper concentrates on the formalism for Gaussian regression problems where prior mixture models provide a generalisation of classical quadratic, typically smoothness related, regularisation approaches being more flexible without having a much larger computational complexity.