Trapping in the random conductance model

We consider random walks on $\Z^d$ among nearest-neighbor random conductances which are i.i.d., positive, bounded uniformly from above but whose support extends all the way to zero. Our focus is on the detailed properties of the paths of the random walk conditioned to return back to the starting point at time $2n$. We show that in the situations when the heat kernel exhibits subdiffusive decay --- which is known to occur in dimensions $d\ge4$ --- the walk gets trapped for a time of order $n$ in a small spatial region. This shows that the strategy used earlier to infer subdiffusive lower bounds on the heat kernel in specific examples is in fact dominant. In addition, we settle a conjecture concerning the worst possible subdiffusive decay in four dimensions.Comment: 21 pages, version to appear in J. Statist. Phy

Random walk on the range of random walk

We study the random walk X on the range of a simple random walk on ℤ d in dimensions d≥4. When d≥5 we establish quenched and annealed scaling limits for the process X, which show that the intersections of the original simple random walk path are essentially unimportant. For d=4 our results are less precise, but we are able to show that any scaling limit for X will require logarithmic corrections to the polynomial scaling factors seen in higher dimensions. Furthermore, we demonstrate that when d=4 similar logarithmic corrections are necessary in describing the asymptotic behavior of the return probability of X to the origin

Evidence of hydrogen content and monovalent Ni oxidation state in non-superconducting bulk anchored infinite-layer nickelates

Since superconductivity was first reported in nickelate thin films, many studies have been published about this family of materials, and different hypotheses have been proposed for explaining the mechanisms and structural dependence. Here, we report the synthesis of anchored infinite-layer LaNi0.9Al0.1O2.1 and its hole-doped derivatives by topotactic reduction from La1−xSrxNi0.9Al0.1O3 rhombohedral perovskites. LaNiO2 derivatives constitute a new family of high-temperature superconductors, with the same structure as high-Tc cuprates but based on nickel, only showing superconductivity in thin films for now. We describe a strategy to stabilize LaNiO2 derivatives in bulk: the presence of Al at the octahedral sites helps to stabilize/anchor the infinite-layer structure. The reasons for the bulk being non-superconductors are hotly debated in the literature. An important question is whether there is some hydrogen incorporated into the structure during the reduction process from LaNiO3 to LaNiO2, predicted theoretically but not reported experimentally. Our neutron powder diffraction data show that, indeed, hydrogen occupies the centers of the Ni–O squares, and spectroscopic evidence from EELS and XAS suggests that Ni is reduced to the Ni+ oxidation state, consistent with the crystallochemical data. © 2023 The AuthorsJ.E.F.S.R. thanks Dr. Carlos Pecharroman and the Service of IR spectroscopy and ellipsometry of the ‘‘Instituto de Ciencia de Materiales de Madrid-CSIC’’ for FTIR measurements. The authors wish to express their gratitude to the ILL and the European Synchrotron Radiation Facility (ESRF) for making all facilities available for neutron and synchrotron diffraction experiments (ESRF proposal HC-4990 in ID22 and in-house beamtime in BM23). Electron microscopy observations were carried out at the Centro Nacional de Microscopia Electronica (CNME-UCM). We are thankful for funding from the Spanish Ministry of Science and Innovation (MCIN/AEI/10.13039/501100011033) with grant nos. PID2021-122477OB-I00, TED2021-129254B-C21, and TED2021-129254B-C22. J.G. thanks MCIN for granting the contract PRE2018-083398. F.S.-S. is thankful for the grant RYC2021- 033518-I, funded by NextGenerationEU and MICIN.Supplemental information can be found online at https://doi.org/10.1016/j.xcrp. 2023.101724.Peer reviewe

A quadratic upper bound on the size of a synchronizing word in one-cluster automata

International audienceČerný’s conjecture asserts the existence of a synchronizing word of length at most (n-1)² for any synchronized n-state deterministic automaton. We prove a quadratic upper bound on the length of a synchronizing word for any synchronized n-state deterministic automaton satisfying the following additional property: there is a letter a such that for any pair of states p, q, one has p·a^r=q·a^s for some integers r, s (for a state p and a word w, we denote by p·w the state reached from p by the path labeled w). As a consequence, we show that for any finite synchronized prefix code with an n-state decoder, there is a synchronizing word of length O(n²). This applies in particular to Huffman codes

Quantum-like criticality for a classical transverse Ising model in 4–ε dimensions

We investigate the low-temperature critical properties of a classical Ising model in a transverse field. This is performed by applying the conventional Wilson renormalization group to the related Ginzburg-Landau functional emerging from a Hubbard-Stratonovich transformation. Results in 4–ε dimensions provide a low temperature critical scenario very similar to that found for the quantum counterpart. Remarkably, we find that the discrimination between the two cases essentially lies on the different values of the shift exponent which characterizes the behavior of the phase boundary close to the zero-temperature critical point. This feature suggests that, decreasing the temperature, the observation of different renormalized critical exponents may signal activation of genuine quantum critical fluctuations. Copyright EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2010

Relationship Between Anti-DFS70 Autoantibodies and Oxidative Stress

Background: The anti-DFS70 autoantibodies are one of the most commonly and widely described agent of unknown clinical significance, frequently detected in healthy individuals. It is not known whether the DFS70 autoantibodies are protective or pathogenic. One of the factors suspected of inducing the formation of anti-DFS70 antibodies is increased oxidative stress. We evaluated the coexistence of anti-DFS70 antibodies with selected markers of oxidative stress and investigated whether these antibodies could be considered as indirect markers of oxidative stress. Methods: The intensity of oxidative stress was measured in all samples via indices of free-radical damage to lipids and proteins such as total oxidant status (TOS), concentrations of lipid hydroperoxides (LPH), lipofuscin (LPS), and malondialdehyde (MDA). The parameters of the non-enzymatic antioxidant system, such as total antioxidant status (TAS) and uric acid concentration (UA), were also measured, as well as the activity of superoxide dismutase (SOD). Based on TOS and TAS values, the oxidative stress index (OSI) was calculated. All samples were also tested with indirect immunofluorescence assay (IFA) and 357 samples were selected for direct monospecific anti DFS70 enzyme-linked immunosorbent assay (ELISA) testing. Results:: The anti-DFS70 antibodies were confirmed by ELISA test in 21.29% of samples. Compared with anti-DFS70 negative samples we observed 23% lower concentration of LPH (P = .038) and 11% lower concentration of UA (P = .005). TOS was 20% lower (P = .014). The activity of SOD was up to 5% higher (P = .037). The Pearson correlation showed weak negative correlation for LPH, UA, and TOS and a weak positive correlation for SOD activity. Conclusion: In samples positive for the anti-DFS70 antibody a decreased level of oxidative stress was observed, especially in the case of samples with a high antibody titer. Anti-DFS70 antibodies can be considered as an indirect marker of reduced oxidative stress or a marker indicating the recent intensification of antioxidant processes