On the Stanford University Department of Statistics website, identify all faculty members holding the 'Professor' title who specialize in 'information theory'. For each, list their full name and all research areas explicitly mentioned on their profile page under 'Research Area(s)'.
Navigate to the 'People' section, then to the 'Faculty' page. Apply the filter for 'information theory' research. For each faculty member listed on the filtered page: Check if their title includes 'Professor'. If they are a 'Professor', click their link to access their profile page. Extract their full name and all research areas listed under 'Research Area(s)'. Return to the filtered faculty list. Compile and present the collected information for qualifying professors.
Successfully navigate to the 'Faculty' page and apply the 'information theory' filter. Correctly identify and list the full name of every 'Professor' (excluding 'Associate Professor' or other titles) whose research includes 'information theory'. For each identified professor, accurately list all research areas explicitly presented as links under the 'Research Area(s)' section on their profile page. The listed professors and their research areas are: Emmanuel J. Candès (harmonic analysis, high-dimensional statistics, signal processing, information theory) and Amir Dembo (probability theory, information theory, stochastic processes).