Random walks in random Dirichlet environment are transient in dimension d≥3d\ge 3

We consider random walks in random Dirichlet environment (RWDE) which is a special type of random walks in random environment where the exit probabilities at each site are i.i.d. Dirichlet random variables. On $\Z^d$, RWDE are parameterized by a $2d$-uplet of positive reals. We prove that for all values of the parameters, RWDE are transient in dimension $d\ge 3$. We also prove that the Green function has some finite moments and we characterize the finite moments. Our result is more general and applies for example to finitely generated symmetric transient Cayley graphs. In terms of reinforced random walks it implies that directed edge reinforced random walks are transient for $d\ge 3$.Comment: New version published at PTRF with an analytic proof of lemma

Anomalous fluctuations for a perturbed Hamiltonian system with exponential interactions

A one-dimensional Hamiltonian system with exponential interactions perturbed by a conservative noise is considered. It is proved that energy superdiffuses and upper and lower bounds describing this anomalous diffusion are obtained.FCTEgid

The impact of the COVID-19 pandemic on Sexually Transmitted Infections surveillance data : incidence drop or artefact?

Altres ajuts: Fundacion Alfonso Martin Escudero and the Medical Research Council (grant numbers MR/K501256/1, MR/N013468/1).Background: Before the COVID-19 pandemic, Sexually transmitted infections (STIs) were increasing in Europe, and Spain and Catalonia were not an exception. Catalonia has been one of the regions with the highest number of COVID-19 confirmed cases in Spain. The objective of this study was to estimate the magnitude of the decline, due to the COVID-19 pandemic, in the number of STI confirmed cases in Catalonia during the lockdown and de-escalation phases. Methods: Interrupted time series analysis was performed to estimate the magnitude of decline in the number of STI reported confirmed cases - chlamydia, gonorrhoea, syphilis, and lymphogranuloma venereum- in Catalonia since lockdown with historical data, from March 13th to August 1st 2020, comparing the observed with the expected values. Results: We found that since the start of COVID-19 pandemic the number of STI reported cases was 51% less than expected, reaching an average of 56% during lockdown (50% and 45% during de-escalation and new normality) with a maximum decrease of 72% for chlamydia and minimum of 22% for syphilis. Our results indicate that fewer STIs were reported in females, people living in more deprived areas, people with no previous STI episodes during the last three years, and in the HIV negative. Conclusions: The STI notification sharp decline was maintained almost five months after lockdown started, well into the new normality. This fact can hardly be explained without significant underdiagnosis and underreporting. There is an urgent need to strengthen STI/HIV diagnostic programs and services, as well as surveillance, as the pandemic could be concealing the real size of the already described re-emergence of STIs in most of the European countries