Path and Method of Urban Carbon Peaking and Carbon Neutralization Based on Random Matrix

With the intensification of global climate change and environmental degradation, achieving urban carbon peak and carbon neutrality has become a common focus of international attention. Traditional optimization methods often overlook uncertainty factors and dynamic changes in data when dealing with urban energy systems and carbon emissions issues. Therefore, this study introduces random matrix theory and proposes a new path and method for urban carbon peaking and carbon neutrality. This work explores the concept of building thermal inertia in depth and establishes a mathematical model of building temperature considering thermal inertia, providing strong model support and theoretical basis for the formulation of optimization strategies for community level integrated energy systems. By analyzing the total and per capita carbon emissions at the provincial level, the distribution pattern of high in the north and low in the south was revealed, and the important impact of climate factors on carbon emission differences was emphasized. Through a double-layer optimization algorithm, we fully utilized the thermal inertia of buildings and achieve more economical carbon emission optimization than traditional algorithms. In addition, we also used the relative index of the Theil index and the absolute index of the Gini coefficient to rigorously test the fairness of the allocation results, and the results showed that the per capita carbon emissions of Chinese urban residents in 2025 after comprehensive allocation were relatively fair. This study not only provides new theoretical support and empirical methods for urban carbon peaking and carbon neutrality, but also helps to promote fair distribution of carbon emissions at the provincial level, providing useful references for achieving national and even global low-carbon development goals.